You sure can. Many bareboat companies organize race weeks. Teams get together and rent a specific type of boat; each day, another leg is raced from one perfect anchorage to the next. You don’t have to be good to enter, just willing. Many are super keen, and the top place getters are cutthroat. Many, though, don't care where they come, its more about the comradery. All the boats are the same, so the competition is close. No spinnaker or poles are allowed.
Racing Regattas is a prevalent activity in Australia per se.
Many of the Caribbean islands have regattas every year where bareboats can enter.