Not at the bare protocol level perhaps but "depending on who gets their hands on [the IP address]" - I'm quite sure your ISP (or someone who can subpoena your ISP) can match that IP at least to your router, your cell carrier can pinpoint you even more accurately. Then there's Google and Facebook and other sites that you use with the same IP and probably hundreds of other ways for you to be paranoid.

Use Tor, that way you only need to worry about NSA and perhaps a half dozen other agencies.