You should have no problem. I was at Carson a few weeks ago for Nats. I was riding EVO CS on my race wheels and my normal Tufo road tires on my spare/warmup wheelset. Both worked fine and I had no problem staying on the track.

I did notice some things though. First, the tires tend to "squeak" when going through the banking at slowish speed. This is the tire scrubbing a bit, something I think all tires do on all tracks at slow speed, but it makes noise on a wooden track. Second, using an alcohol wipedown of the tire before going onto the track, especially after riding aluminum rollers, keeps the squeaking to a minimum and seems to improve grip.

I did see a couple people sliding off the track. Once on a training session, and twice actually during women's sprints. I think this is just technique. Keep your front wheel weighted and keep your speed above traction speed.

I was told traction speed at Carson is 16mph and the banking is closer to 48 degrees rather than a more normal 43 or 45 for a 250m track. Personally, I had no issues with it.