War and battle is not about killing...
Summary / tl;dr
Yes, this military will be effective, because you will write that it is.
Your job as the author is to make it credible.
...it is about control
This is not even a platitude: war and battle is not at all about killing people, war is about establishing and/or keeping control. When you have control you have won the war.
And what is it that the belligerents want control over?
- People, because people can do work and pay taxes; they produce value
- Resources, such as mineral deposits, manufacturing, farmlands
- Areas, strategic locations from which you can conduct operations, or use as transport routes
Now granted, it is "easy" to win control by simply removing someone that stands in your way, for instance by killing them. But killing is not at all necessary to win control. In lieu of outright killing your enemy, you need to either deny them the control they want, or make them unwilling to exert control over your people, resources and areas.
You said that this nation is by far the most advanced nation on the planet, to the point of having self-propelled armoured vehicles a full half-century before everyone else. This means they have two things with which any defensive force can win the war: mobility and communications.
1. Winning the information war means: always ahead of the invader
No matter what the invaders do, it appears that the defenders know — as if by magic — where the invaders are going to turn up next, and they always seems to be adequately prepared for this.
The "magic" in question is things like wired and wireless telegraphs, used by a vast network of observers, informants and agents. While the invader is on foreign soil, they have to rely on messengers to deliver physical messages, and all attempts at establishing instant messaging like a telegraph network is always thwarted by the defenders.
2. Nothing to control
Whenever the invaders show up at what they thought was a significant location, there is nothing there to control. The civilian population has been evacuated and relocated with astounding efficiency, the advanced machines that your nation is famous for have either been moved away or dismantled and hidden well, the invaders find mine shafts filled with water and no way to pump it out, the granary cashes remain empty or simply never found.
With few people in this defence force tasked with battle you get a lot of people available for preparations and transport. And even more people available to train and drill civilians in how to quickly and efficiently be relocated, out of the way from the invaders.
3. Disrupt logistics routes
"Amateurs talk about tactics, but professionals study logistics."
General Robert H. Barrow, Commandant of the Marine Corps, 1980
No invading military has ever been able to maintain control if cut off from their home-land. Your nation's defence has specialised troops that excel in messing up supply routes for the invading enemy, denying them food, resupplies, and — maybe worst of all — a way back home. That impressive iron bridge they invaders passed over yesterday? It is now a pile of mangled beams at the bottom of the ravine. That nice paved road through the marches? It got flushed away by an unnaturally appearing flood that soaked that whole area and made the roads completely impassable.
The invaders may get into the country with relative ease but once there the initial victory rush will be replaced by being bogged down in a logistical nightmare. This point and the one above would not be the first time in history this has happened.
4. Psychological warfare
— Hey, did you hear what happened to the captain's previous command?
— No, what?
— They disappeared... all of them. He went to sleep one evening in the camp... the next day... poof they had all vanished, like magic. Only he and his tent was left standing.
— You are pulling our legs...
— Try, ask him... see how he freaks out.
Sleeping gas and nets? Specialised in rounding people up and taking them captive? You nation's defence will be experts in cooking up all sorts of "mysterious" events that — when re-told by influence agents hidden in the invader's ranks — will demoralise the invaders really quickly, especially when cut off from home as mentioned above.
Add to that effective propaganda, outright bribes of entire military units, impressive — and frightening — displays of technological aptitude and skill, and you can soon have invaders that shivers at the kneecaps at the thought of trying to deal with this enemy.
One of the biggest demoralising elements of this is that the invaders are simply is not prepared for this. They have trained for traditional battle, of setting up face to face in the field and then clashing together. Nothing(!) prepared them for an opponent that behaves like this; they are not being out-battled, they are being out-manoeuvred.
The final blow is when the diplomats — with a confident smirk — convey the message: "And if you think this is bad, just imagine what happens when we decide to use force. I advise you to go back to from whence you came while you still can. Good day gentlemen, ma'ams".
5. The ultimate ace up the sleeve: author's say-so
In the end it does not come down to whether a non-lethal military would be effective in real life or not, but whether you as then author can make it credible; if you can make the reader willingly suspend their disbelief. This military — in your story — will be effective because you as the author will say that it is. The only issue is if you can get the reader to accept it.