It is a kind of crutch, but it depends on what you expect from online chess.
If you use it as a substitute to OTB play (to play long games), then I would recommend not using the analysis board.
If you use it for research purposes, or for fun, then why not use the analysis board.
I am new to chess.com, and after a 3-0 start my online rating is well into the 1500's. I am regularly using the analysis tool during my games to study various lines of play - it's like using a second set during a correspondence game. However I'm concerned it will become a crutch. In your opinion, is relying on the analysis tool an issue? Should I be playing as if it's an OTB game and calculate variations in my head? Any advice is appreciated.