technically you can. why? 2 words: Satoshi Nakamoto.
It's arguable that the things that Satoshi has never actually implicated his real life identity. His likely use of a VPN/Tor has probably made it much more difficult for people to trace him. His involvement in Bitcoin was primarily on the development and his use of obfuscation techniques probably helped his anonymity tremendously.
I doubt that would be the use case of an average joe when they use Bitcoin.