Is there any research/evidence that would indicate that training (drills, katas, etc rather than sparring) for martial arts more broadly (striking arts like TKD, Karate and Muay Thai more specifically) while wearing weighted clothing/sleeves is beneficial in terms of speed, technique development, etc? Conversely, is there evidence that training in this way is detrimental?
There are a couple things that I would caution you about when using weighted clothing and/or bands.
If you use a vest or other close to the body clothing, you may notice slight balance issues, and you also increase the landing impact when doing jump techniques. The other consideration is that by weighting the limb, you may make the technique slightly stronger, but you may also impact the speed. They have done studies with baseball players showing that by swinging 2 or 3 bats (extra weight) or a weighted bat as a warmup, you actually slow down the swing speed of the batting session.
I know people that do train this way, and they do all right, so as long as you are aware and cautious and take the time to work weightless as well, you should be all right. I personally would just do supplemental weight training, but if you are time crunched I can see some benefit.
Weighted clothing is not particularly useful since its benefits in terms of resistance are inversely proportional to how much it upsets your sport-specific movement. Put simply, it's not heavy enough to make you stronger, and if you do make it heavy enough, then you're practicing bad technique and making yourself tired without getting that much stronger or faster. Coach Izzy explains:
If you want to get stronger and faster, start a strength and conditioning program that includes power training. If you want better technique, do technique work under circumstances as close to application as possible.