Aero bars can be made to fit. I used to have a set of clip on aerobars for years on my mountain bike when that was my only ride. They were primarily for comfort, to rest my back and arms during a long ride but were nice to help tame headwinds.
If you do mount clip ons, look into other adjustments, like flipping the handlebar stem and sliding your seat forward or even rotating the seatpost 180 degress.
You will benefit by getting lower, I imagine that you will see a significant speedup with aerobars and some other tweaks to get the fit right. As mentioned previously, you need to get some hours in with the new setup to be both comfortable maintaining the position and getting used to the handling before a race. Your hands will not be close to the brake or shift levers for most of the race.
For your bike, you probably want the areobar types which are not bridged so that you can make the spacing work with your brake, shift levers. Models like the profile design century are more or less fixed in spacing and may not be compatible. I used the profile design "Jammer" areobars on my mountain bike.