I can pretty much guarantee you will not be the only one with a non-traditional road bike for your first tri. My wife's first one, there were more than a few Target/Walmart MTBs, complete with knobbies. At my first one, in addition to the usual complement of MTBs, a guy was riding a folding bike with 20" wheels.
Ride whatcha got, and decide if you want to invest in a tri-specific or road-specific bike later.
Jim