No it's not... the wiki mentions certain scenes that only proc if she's caged, as future-proofing for when she isn't. Nowhere does it say 'Hey, you can totally remove it now'.
Actually taking the cage off requires either Alissa's lethicite (which isn't in the game yet) or for Lumia to remove it (which isn't implemented yet because the bulk of the post-uncaging content is being written for the former option).