I've never known any cycling race to not allow the use of a flash, but it's a good idea to ask first if you're not sure. I asked when I shot my first cycling event which was a cyclocross race and it was fine. As a Mtn biker I can tell you that you don't even notice the flash going off while you're riding. Obviously I would never flash it directly into a rider's face. I never use ETTL or Tv. I'll use Av only if the lighting is changing too fast for me to deal with shooting manual, but I've never shot in anything other than manual when using a flash. If it's dark and raining the lighting should be consistent so you should be fine. Also, I always use the flash off-camera so that means using the flash in manual as well. I'll normally underexpose the ambient by 1-2 stops depending on what I'm looking for and adjust the flash output accordingly. This will help separate the riders from the background and make them pop more. This also allows the speed of the flash to freeze the action despite your slower 1/200 sync speed. If possible, I'd just have someone stand where the cyclists will be and do some test shots on them before hand if you're worried about getting the exposure and flash output correct. At the very least I would play with your flash before the race to make sure you're comfortable with what you're doing. Don't wait until the race to try and get everything figured out. If you're lucky and get the same weather conditions a day or two before, that will be ideal for you to practice this. Here's a good thread worth reading about using flash for night football: https://photography-on-the.net/forum/showthread.php?t=564413
