Yes, it seems that Gothel went to the same parenting classes as Frollo (less the sideline in genocide and religious fundamentalism), and has manipulated and emotionally blackmailed Rapunzel into staying in the tower for her own safety, becoming sarcastic and snide whenever the subject is breached and baulking at the idea of Rapunzel surviving on her own. She then launches into a passive-aggressive song and rounds it up with veiled threats if she ever asks to leave again. So, that would be a no.