If your sawblade will not shatter, it should be fine. Basically anything that's not hardened steel or angle grinder discs shouldn't shatter, though make sure you check before you buy. Tempered steel should be fine, you just don't want hardened steel that will explode and send shards of very sharp metal flying in all directions. That said, it's totally down to the event organiser, so you'll want to ask them before you sign up.
Sawbots are on the up recently, seemingly inspired by the success of bots like Red Devil, Skorpios and Sawblaze, so of course a circular saw is in the spirit of the competition. As for what competitions you want to use them at, I'm not sure if sawblades are allowed at non-spinner events, since they're quite damaging but they don't carry a lot of inertia like most spinning weapons. A sure bet would be an Extreme Robots event (which allows spinners) or if you're in the Leeds/Sheffield area, Robodojo has promised a spinner-capable feather arena by October. Best of luck with your build!