In smaller local races (especially sprints), you'll find a lot of hybrids and MTBs along side the road bikes and tri bikes (though it can depend a bit on the specific race). You will be fine to do races on almost any bike though. As was mentioned, too hard a gear can kill your bike and/or run, so if you can try to pre-ride the course to know for sure.

If you're unsure about the "competitiveness" (i.e. mix of super serious athletes and recreational ones) or the terrain, give the RD a quick email/call and I'm sure they'd be happy to answer.