It depends on what's punished ...
Is having an impure or fleeting thought punished? For example: say I'm at the store, carrying a small item I intend to purchase; if the idea "I could just walk out and nobody would be the wiser" crossed my mind, is that punished? ... what about if I - with no intention of actually stealing the item - look around a bit to see if there are security cameras or people watching and think about where I could hide the item?
Crank that up to higher levels, too: if I think about how I might kill my annoying neighbor (who mows their lawn at 7:00 am on the weekend?!?), is that a serious crime?
If thoughts are punished, there is a 0% chance of "crimes" disappearing.
Everyone will, at some point, have impure or fleeting thoughts. It's entirely possible that some of the most upstanding members of society will have a lot of them (to their credit: refusing to succumb to temptation is surely karmically better than not being tempted in the first place). If thoughts are punished, everyone is going to get those light punishments, which will weaken the threat/stigma of punishment (lots of people get light punishments, which means that light punishments aren't seen as "bad" - as a real-world analogy, consider most crimes that come with a fine of less than, say, $500 - even people who rack up parking tickets are rarely seen as "bad" because of the tickets).
How do extenuating circumstances factor in? Is stealing a loaf of bread to feed a starving family a punishable offense? Is withholding a loaf of bread from a starving family punishable? ... what about dine-and-dashing if you're broke? ... what about stealing a car to get your injured wife to the hospital? ... what about killing in self-defense?
And, does state of mind matter? If I don't intend to steal the candy bar, but just get distracted and forget I'm holding it 'til I get home (which I can 100% see some of my actually-diagnosed-by-a-real-doctor ADHD relatives doing), is that as bad as intentionally stealing it? ... what if I think I've grabbed my taser but actually grab my pistol and shoot the intruder?
It's easy to see a scenario in which the complexities of thoughts, intent, and extenuating circumstances either overwhelm the system (thus rendering "you got punished" all but meaningless since it's so very easy to suggest that the system got those complexities wrong) or where those complexities are ignored (thus rendering "you got punished" all but meaningless because of a lack of mercy, compassion, and/or nuance in the punishment system).
... and the punishments...
If the punishment for murder is a night in the pokey, very few people will be dissuaded from murder simply to avoid a night in jail; little or no crime is prevented.
If the punishment for littering is death, very few people will be dissuaded from escalating from "my neighbor is annoying; maybe I'll pour some sugar in his lawnmower's gas tank" to "I'll just kill him" simply to avoid the additional punishment - there can be no additional punishment, really - so crime might actually go up (or, at least, the severity of crime).
That's not to say that everybody with an inconsiderate neighbor will become a murderer, just that those who might be inclined to be murderers anyway but are dissuaded from killing by the fear of punishment are apt to be less dissuaded (and possibly more likely to give into their urges, since the difference between "sugar in the gas tank" and "hedge clippers in the heart" is nonexistant).
... but probably not.
In addition to the above, there will always be a market for those who are willing to do the illegal - even if there's a high chance of getting caught and punished - in exchange for power, prestige, wealth, likes, etc..
Consider a terminally-ill individual without any outward sign of being ill. If I offer to give their family \$1 million to kill my lawn-obsessed neighbor, sure most might decline, but some wouldn't. And, I've now "murdered" my neighbor without actually killing anyone and increased my karma by gifting the family of a random stranger $1 million after said stranger passed. Go me.
Unless, possibly, the system is 100% perfect.
How does the system handle the criminally insane? ... or just those with run of the mill mental health issues who might have gone off their meds (or need their meds adjusted), and/or have (for whatever reason) missed some psychotherapy appointments? ... or those who haven't been (properly) diagnosed?
A relative of mine has been clinically diagnosed with a handful of mental health issues, which all feed into one another to varying extents. Not long after a particularly stressful time, something snapped. We were sitting next to each other (as we do frequently); whatever snapped made them think that I was a danger (as near as we can tell now, looking back on the event) and they started hitting me, trying to "get away". I could technically have filed assault and/or battery charges; from a purely legalistic perspective, they did hit me. But: that would have helped nobody, and it wasn't assault or battery in any meaningful sense of the words; it was just someone who desperately needed professional medical help run out the timer on their ability to pretend that everything was status quo. To round out the story: they went in to the psychological wing of the emergency room for a few days, until a bed opened in an excellent in-patient program the hospital offered; they got some meds tweaked and the psychotherapy they needed to get back to actual status quo, and fortunately haven't had a relapse sense.
If the system punished that relative for the "crime" of pretending everything was okay when it really wasn't (and, let's be honest: every single person reading this answer has done so at some point), the system is fundamentally broken and any punishments it hands out are utterly worthless as a measure of the "goodness" of the recipient.
If, however, the system were magic and able to determine correctly which crimes were crimes of passion (which is a whole 'nother kettle of fish), crimes of desperation, crimes of accident (the aforementioned "I forgot I had the candy bar"), not-actually-crimes (my relative didn't assault or batter me, even if their actions met the literal terms spelled out in the legal codes), premeditated crimes, and proxy crimes (that \$1 million payout to the family I offered earlier), then maybe - if the punishment ensured that the offender was no better off than they were before the crime.
How would the offender be better off? If they get to keep the \$1 million they stole from the bank and just have to spend a week in jail, they're probably better off - doubly so if (eg.) they're part of a gang that won't "fire" them for missing a week's work (they didn't miss work; their job that week was to sit in a cell and not cause problems).
I have a lot of other questions, a lot of which revolve around what evidence is required to convict someone of a crime. If it's just the karma tracker, how hard is it to fool (or tamper with!) the tracker?
How do conspiracies work? If I chat with my friend about how to knock over the local convenience store with no reason to believe they actually have the intention of carrying out the plan, am I still guilty of something? What if the discussion is (eg.) in the context of a role-playing game?
How are accidents resolved? If I'm roofied but don't fall asleep until I'm driving home, who's responsible for the mailbox I hit? ... what if I just fall asleep because I'm a lot more tired than I thought I was? ... what if I have an unknown medical condition or a medical emergency that causes me to lose control?
What happens if I do something heinous while sleepwalking?
How well can the tracker (etc.?) handle code words and innuendo? ... "I'd like you to take care of my neighbor" could be code for "kill him", but could also just be a request to convince him to wait 'til a more reasonable hour to mow the lawn, or even mow the lawn for him Friday while I'm out at work! ... what if that innuendo is taken the wrong way (if I meant "mow the lawn Friday" but Joey thought I meant "whack him")?
Is pre-crime punished? If the system can detect that I'm actually planning to kill my neighbor - with intent to do so - does it stop me before I can enact my plan?
This reminds me of Minority Report (Philip K. Dick), The Memory of Earth (Orson Scott Card), Gattaca (1997 movie), 1984 (George Orwell), and Isaac Asimov's robot stories. All of those works (and, I'm sure, hundreds of others that I've either forgotten about or haven't experienced) poke at different aspects of this technology/society.