What side effects would occur if you were to go off birth control with pcos?

Same. Mostly the same ones you had before you started pills. Iregular/skipped periods are the most common; acne, facial or chest hair are also very common.
Relapse. Most women with pcos do get good results for cycle control with birth control pills. Ehen they decide to stop the pill, most of them will eventually resume the irregular cycles the experienced before using the pill.