Alex Skolnick shreds on LP type guitars with no problems. He is the first that comes to my mind. Others can shred a Les Paul too, like Al Di Meola, Neil Schon, Zakk Wylde, Randy Rhoads, John Sykes, Matt Heafy, John Norum, Rik Emmet, Doug Aldritch, Buckethead...
So it is possible