No he doesn't. We're all going to be disgusted if Josh doesn't win a Super Bowl, let alone win one. However, I think 2 more years of the typical seasons he's had for the last 5 years makes him a shoe-in 1st ballot HOFer... Super Bowl or not.
And truthfully, I think if his career ended tomorrow (God forbid!!!) he'd still get in, but maybe not 1st ballot.
My argument?
Find a QB in NFL history who even comes close to the 5 consecutive year stretch Josh just had.