Legally it shouldn't matter, but it does indicate that the guy wearing it is a lying scumball, and he should expect any non-legal consequences like getting the crap beaten out of him if his lies are discovered. The first amendment protects free speech from government interference (except when telling the truth about an incumbent during election season - thank you rino Juan McCain) Doesn't mean that there shouldn't be non governmental consequences.
I don’t grok this angle on the case. The beating was clearly contrary to established law under any conceivable circumstances (I’m not hearing about any citizens arrest which it was necessary to effect by said beating). I have no sympathy for the chesty thumpers should they be hauled in on charges by police and convicted in front of a black female Clinton judge. With that said it ought to be considered fraud and civilly actionable to obtain favors by false pretenses no matter if you’re impersonating a general or a handicapped person.
But the scumbag took/received gifts based on his lie. He conned people. He should be liable, imo. Otherwise, if he announced that it’s fake, and then received the gifts, it’d be ok.