It wouldn't have changed a thing. Everybody knows you "leave the gun, take the cannoli". The reason he kept his supposedly untraceable gun with him was he intended to be caught and wanted there to be no doubt that he was the guy. He even had his manifesto printed out and ready for the cops to find.
This appears to me to be a calculated attempt at propaganda of the deed. Propaganda of the deed is supposed to incite "the spirit of revolt". This is not supposed to end with him being caught; he knows perfectly well killing one CEO won't change things. Other people are supposed to copy him.
Deliberately getting caught is an interesting twist. If there had been an extended manhunt, the public focus would have been even more on the perpetrator, and when he was eventually caught after a long and satisfying search it would be over. The fact that it wasn't that hard to catch him means that the frenzy wasn't done building yet, and puts more focus on his motives than his identity.
I think the 3D printed gun was intended to underscore the fact that there's nothing the establishment can do to stop anyone who has got the idea of direct action into his head.
Read this guy's biography on Wikipedia. He's no dummy; I think he thought through every aspect of this to maximize its impact.