Well it can strongly be inferred considering that most of the systems the Empire took over hated being under their rule and opposed them strongly, however they would get in trouble if they opposed the Empire publicly so basically the answer is yes.

If systems were allowed to leave the Empire most systems would have and the Empire would’ve been much smaller from the get-go. Ezra wouldn’t have spent 4 seasons trying to free Lothal, Cham Syndulla wouldn’t have spent over a decade trying to free Ryloth, hell the Rebellion would have less reason to resist if planets could just leave freely. No one needs to directly say that systems weren’t allowed to leave the Empire because saying so would be like saying “The sky is blue”. Everyone knows it, otherwise the galaxy wouldn’t be in the state its in and the characters’ actions wouldn’t make sense.