Ex-uni fencer here. Yup, yup and yup, especially if the person in question isn't just some rando but an actual fencer who trains and competes.
In the end, all that matters is that you hit your target before they hit you. That's why we have electronic rigs that measure that for us, because it's usually not possible for the human eye at a high level. Near-simultaneous touches are common and every millisecond will count.
Remember; there are three kinds of fencing. Epee, foil, and sabre. This may have a small impact on what you're doing.
The different swords.
In epee fencing, the goal is to hit 'em with the pointy end, literally anywhere on the body. The sword is the longest of all three, and more firm than flexible.
In foil fencing, the only valid target is the torso, including the groin, not including arms, legs or head, and again, you use the pointy end. The sword is the shortest of all three, and exceptionally flexible.
In sabre fencing, the target area has increased to "anything above the waist". The sword is between foil and epee in length, with a slight curve, and typically fairly rigid. In sabre, we slash instead of stabbing. Think pirate fights.
Advantages and disadvantages
I would expect increased speed to have the least benefit in sabre duelling, because the slashing technique lends itself to larger blocking arcs and more back and forth. Though, sabre fighters are notoriously... violent in technique. Long charges forward and sharp "samurai-style" cuts down upon the head for instant victory are fairly common.
In epee duelling, I would probably expect the most benefit. Many epee duels end with touches the opponent's toes, because everything is a target. If the duellist is accurate, they're likely to win every single time. However, the sword is quite heavy and rigid, so it tends to be harder to reorient and change its momentum.
In foil duelling, I would expect an extreme advantage, but probably less than in epee. This may be an unpopular opinion, though. The foil is an extremely dextrous and agile weapon, and foil is all about speed. But, due to the shorter sword, closer distances and smaller target area, I would also argue that, as your fictional fighter doesn't possess increased reflexes, their increased speed may be of slightly less help.
Summary: Your guy probably crushes everyone.
Ultimately though, I would have to say that all of these are subtle differences that are unlikely to matter, because a speed increase of 200% is such a phenomenal advantage, that against a normal opponent, I would expect your character to essentially win every single time.
I am open to being challenged on this. I once had the pleasure of wheelchair fencing a silver-medal Paralympian. On his first attack, I didn't even see him move, I just felt horrible pain as he whipped me directly in the vertebrae. He was that quick. So, up against Olympic-grade athletes, the tables may balance somewhat.
Hope any of this is useful!
Addendum 1: Momentum
One thing to question is whether the increased speed comes with increased torque. Do they have more strength?
If yes, don't worry, they'll rock everything. If no, a small problem emerges.
Let's say your dude thrusts with the sword, three times faster than normal. Well, they'll also need the grip strength to maintain a grasp on a heavy sword travelling that fast. Just a thought.
Sub-addendum: Forces and Damage
One thing you may also wish to consider; if you choose to give your fencer the additional strength/torque required to handle objects at their increased speed, one issue may come up.
Your guy may actually find themselves breaking swords, or possibly even striking lethally. While the safety gear is pretty tough, injuries do happen, especially if the sword breaks or the gear is damaged, and at 3 times regular speed, you're looking at 3 times the regular force being delivered.
As @Oddrigue has pointed out, body-to-body contact in fencing can get you penalised. Consider that, as a triple-speed lunge is going to impart a lot of momentum on a body. This has to be balanced and corrected to avoid tumbling forwards.
Addendum 2: Reaction Speed
I covered this somewhat above but I felt I should clarify something.
The reason reaction speed shouldn't matter much in fencing (which is amusing in and of itself) is that it's first blood that counts. All your guy needs to do is make the first move every time and they'll be fine.
In a situation where they're on the defensive though, they'll struggle much more. Reaction speed is more important to your defense than "ability to move a sword quickly".
But, with even a basic sense of offensive strategy, they should dominate at an Olympic level without breaking a sweat.
Addendum 3: Priority
This one completely slipped my mind, but as @Nobody in the comments pointed out, in foil and sabre fencing, there is a system called priority, and touches that both land within a second of one another are settled via this system. Occasionally, the judgement here is a simultaneous touch.
In epee, you don't need to worry about this at all. Stick 'em with the pointy end.
In foil and sabre though, this is going to have a major impact on your fencer. They may potentially lose a lot of points to simultaneous touches, and without quick reflexes, they may even lose points on priority.
I still think that the advantage would be overwhelming, but this definitely balances things. As @Nobody has opined, it could actually be make-or-break at the Olympic level.