Nope.
The whole "Paul McCartney is dead" thing really took off thanks to wild conspiracies dreamed up by people spending far too long studying the Abbey Road LP cover. Paul is barefoot on this, apparently a sign that he was dead (actually, it was a hot day and he had removed his shoes to cool off). Part of the numberplate on the VW in the background reads '28 IF' - taken to refer to the fact that Mccartney would then have been 28 years old, IF he had lived. Just people ingesting too many 60s substances if you ask me. As for Billy Shears, as far as I know he was just a fictitious character name-checked on the Sgt Pepper album at the end of the title track (just before Ringo ploughs in to With a Little Help From My Friends).