Sure they can. When they find your fingerprints on it, your name on the bill, people willing to testify that they consider the number that the phone is associated with to be yours, etc.
It's not bulletproof like some sort of mathematical proof, but the law operates with much looser standards of proof.
Then there's the case of destruction of evidence. Depends on a number of circumstances, possibly including whether or not it takes a positive act or merely the lack of an action, on your part, to ensure the data continue to exist.
There are so many things that can be done digitally that bump up against the first, fourth, and fifth amendments as well as laws about the destruction of evidence. It's a mess.
Are you asking what would actually happen if you did this, or what would happen if you told the courts that you could not let them into your phone because you did this?