Depends what distances are You up to and in what weather. If You bike in warm weather and can simply dry off at home / in a hotel after a race, than no big deal. The cycling jersey might do just fine with some basic windbreaker against the chill.

Shakedy is however a gamechanger for anyone doing ultra distance and self supported racing. The ability to bike through a rainy night without worrying about Your upper body being wet is nothing short of amazing. And I say that as a proud owner of a not-too-old Goretex Pro mountain jacket and some older membrane jackets before that.