Highly unlikely. However, shooters like Elliot Rodgers are actually considered a hybrid serial spree killer, which is rather new I believe. He was a serial killer arguably because of the cool off periods; however, disorganized serial killers have similar short cool off periods, but his were even much shorter to the point he was like a spree killer almost, other than for that spree killers don't typically have cool off periods.
So, guns may have ushered in an era of a new sort of spree serial killer; however, the psychology of what is classically thought of as serial killing is substantially different from that typically associated with spree killing, other than arguably for disorganized serial killers, given their short cool off periods, but they are still more Son of Sam than Elliot Rodger, who was similar to a disorganized serial killer, but somewhere between them and spree killers.