I would look into the local cycling clubs and local USCF (United States Cycling Federation) racers who could offer insight into training on a velodrome and the difference between training for road races vs. track races.
Track races are usually shorter than many road races, with the shortest being the match sprints (3 laps, with the first 2-2 1/2 being as slow as the two riders want) and the kilometer (aka "killermeter) time trial, which lasts a little over a VERY painful minute for the fastest riders. If you've got the fast twitch fibers, go for it.
The only reason I'm explaining this is that training time for short events is less than that of the road events. Too many cyclists put in miles and miles of long distance riding, only to loose the race in a sprinting effort they haven't trained for, like myself at one time. If I had to do it all over again, I would spend more time working on the power, speed, and explosiveness that track cycling is good for, rather than junk miles out on the road.
Enough rambling, I do think you'll enjoy riding on a velodrome, especially if you like riding a fixed gear bike. A lot of guys I raced with used to ride a fixed gear in the off season to smooth out their spin and for a change of pace. Having a velodrome to play on just makes it more fun.