No. A ton of excellent QBs never won a ring. Especially in days before Free agency started. I always thought Archie Manning was way better than all the teams he played for. Dandy Don Meredith deserved better. The old Baltimore Colts QB Bert Jones was really good but never had playoff success.
And a lot of average to above avg QBs have rings because they were part of an outstanding team. Guys like Phil Simms, Jeff Hostetler, Jim Plunkett, Mark Rypien, Joe Thiessman, Trent Dilfer, Brad Johnson and more recently Nick Foles were not anything more than above average QBs IMO.
Winning a SB is certainly a great accomplishment for any QB. But it’s not everything.