Let's say Mallory puts on makeup to look like a celebrity, maybe even the president of a country, and goes around sounding and acting like that celebrity. He goes to events where only the celebrity would be allowed in, gets free stuff, does some bad things in public. However, he never claims that he's the celebrity in question, maybe even (jokingly) saying he's not that celebrity, just letting other people assume his identity.
Would such an act put him in legal trouble like for identity theft?