Not exactly the same. "Can I take this thing off yet?" is asking if it is ok to take off now - rather then later. "Can I take this thing off?" is only asking if it is ok to take off - it might imply now, but its not explict. Example Conversation: A: Can I take this thing off? B: No. You can take it off later. .... time passes ... A: Can I take this thing off yet? B: Yes

Can I take this thing off? ---> You just want to know if you can take "this thing" off. Can I take this thing off yet? ---> Implies that "this thing" has been there for a while and you want to know if you can take it off.