The tails distro is setup to not remember anything once it is disconnected from the host computer. So each time you would have to redownload the entire bitcoin blockchain all over again which is very inefficient. You could however setup a permanent encrypted drive within tails to store the blockchain. The question then just becomes can you be 100% sure that you can force the core client to ONLY use the tor connection without going around it? If you have the programming know-how to do so then yes you could potentially do that.
I recommend just using the electrum that they have embedded in tails so you know that it wont bypass the TOR connection and reveal yourself.