Being now in my 3rd real season of track sprinting, I've sorted out what seems to work and what doesn't at least for me. I have really been more of a kilo guy, but can run an outdoor, sea-level, concrete, 333m track 200m tt in 11.1.
Remember always that cycling is power, not strength. The most impressive gains I've made in power on the bike included exactly zero gym work. It consisted of very intense sprint work and starts on the track bike. I dropped a full second off my already ok 1/2 lap start in 6 weeks. That says to things: 1) I had a lot of genetic potential left, but 2) That on-the-bike training is awesome for being on-the-bike fast 😉
There is certainly merit to doing gym work, but it is not that it makes you faster as a sprinter. By itself it might make you slower. What it does do is makes more muscle - and fast twitch at that. After the gym phase, when you do get on the bike there's more to work with. Mostly you'll be training those new fibers how to fire in new patterns.
One more note on gym work - it is nearly impossible to do long hours on the bike concurrently with strength training with the goal of hypertrophy (muscle gain). There are only so many hours in a week for your body to recover. The two ideas are nearly in direct opposition. Once the muscle is there, maintaining it is easy with minimal gym work, but the building phase necessitates backing off quite a lot on bike time. A bit of a trade off, but consider it an investment for the future.
Train on.