Nope. It is always possible if you have a smart personnel man and a good owner.
After 2000 SB win, the Ravens cut about 19 of their 22 starters and were competitive within 2 years without a franchise QB. Key is a good personnel man and a good coach in turning the team around, and the personnel man is most important. Not that a coach cannot be a good personnel man.
You can always get players. The league is full of players tht were cut and picked up for short money that turn out to be good. You can always cut deadwood. A good QB is a good thing to have, for sure, but again it is a case of being personnel smart and getting one with the resources you have.
That's why I say a GOOD personnel man can turn a team around in two years.
If you have to convince the owner, that is a big problem. That's why I said having a good owner is more important than good players when you take over a dud team. You can change the players, you cannot change the owner.
The draft is designed to help bad teams. Some teams remain bad for years, and the problem is at the top. A bad owner negates everything below.