Even if he doesn't win a super bowl, I feel like the only record he wont pass Kelly in is the number of consecutive superbowls they have appeared in.
He's likely going to pass him in TD's (134 short right now). He's been over 35 the past two years so that's only 4 years if he keeps that pace. Yards, ~14000 to Kelly's ~35000. Comparing the 4 years for Allen and 10 years for Kelly, he's already averaging the same amount of yards per season (~3400-3500). And the last two seasons for Allen were over 4.4k.