Yes, both nationally and internationally. There's a UCI Grand Tour road race going on right now, the Giro D'Italia in Italy. Before the start of every stage, they start a stage of the E-Giro, an e-bike road race. They will race a similar course. E-MTB racing is also a thing. E-MTB's race in their own class. Some races have two E-MTB classes, Open (<=750W) and Unlimited (>750W). Gravel races are starting to add e-bike fields as well.