Can I race on an endurance road bike?

Absolutely. Many riders complete gran fondos, club races, and even criteriums on endurance bikes. The handling is stable rather than razor-sharp, which is a disadvantage in tight criterium corners but an advantage in mass-start events where predictability matters. If you are new to racing, an endurance bike is a fine starting point. As you gain experience and discover you need a more aggressive position or sharper handling, you can consider a race bike later.