Historically, QBs drafted #1 overall very rarely bring Super Bowl success to the teams that drafted them, or in the case of Elway and Eli, their original teams. Below is the list of every QB drafted #1 overall in the Super Bowl era and if they either win a Super Bowl for their original team or at least played in the Super Bowl for their original team. (So no Stafford with the Rams)
Won Super Bowl(s)- 5: Bradshaw, Elway, Aikman, Manning, Manning
Won Conference Championship-4: Bledsoe, Newton, Goff, Burrow
No Super Bowl Appearance- 15: Plunkett, Bartkowski, Testaverde, George, Couch, Vick, Carr, Palmer, Smith, Russell, Stafford, Bradford, Luck, Winston, Mayfield.
TBD-3: Murray, Lawrence, Young
So out of the 27 QBs drafted #1 overall, more than half never even made a Super Bowl for the team that drafted them.
TL:DR: Drafting a QB #1 rarely means any success.