Let's say that Mangione committed the crime.
My understanding is that he gave cops a fake ID when they questioned him on reasonable suspicion (the basis of which was a tip from an employee). That is something that yes, he can be arrested for. And he can be personally searched after that arrest. But at that point, he can no longer get a gun out of his bag, and cops have control of it, so he can't destroy evidence/get a weapon from it; so searching the bag should be out at that time. So, my understanding, based on case law, is that they would have needed a warrant to search it at that time, as the contents of the bag aren't related to the reason he's been arrested. You aren't supposed to be able to use a pretextural arrest to search a person's car or belongings (e.g., arrest you for suspicion of drunk driving, then search your car to find evidence of burglaries).
In theory, without the warrant, the search and everything from the search should be out. Even if he committed the crime, and kept all the evidence conveniently in his backpack, it should be completely excluded from the case. I'm sure that the DA is going to argue that there's some exception that allows a warrantless search, but I can't say what that argument will be. If the evidence is allowed in, his defense attorney is going to have to object every single time that prosecutors refer to it, for any reason, in order to preserve the option to claim that evidence was improperly admitted in an appeal. (Which they should absolutely do, if it goes that far!)
Federal rules of evidence is pretty complicated stuff. But goddamn, does it look like someone fucked up bad on a really high profile case.
