I think the league would stop it but it would be viewed as unfair to the coaches as others would be getting those interviews. They would need to put an entire new system in place where you cannot start interviewing anyone for coaching and GM vacancies until after the super bowl.
That's why I'm saying that the best solution, imo, is to have a coaching window like they do for trades and FA. They could really have fun with it. The week after the SB, the coaching window opens where teams can interview coaches and hire them. Then, they can do the Senior Bowl the week after. The week after, open the trade window, before finally opening the FA window after that leading into the Combine and the draft process. Doing that would mean that they still dominate the offseason.
Beides, if they're interviewing and hiring coaches prior to the SB, what happens if a coach retires after winning the SB? Say, hypothetically, that we win it and Mike McCarthy decides to retire. Without the window, we'd be stuck with the rest of the litter. By doing it by way of a coaching window, then it leaves the possibility for SB winning teams to also be able to have their choice of coaches too, should the HC retire after the SB.