It would, of course, depend on who Bama hired to replace Mike Shula. But not as many as we do now. Before Saban arrived we were one of those old school blue-bloods living on old glory days.
In the 10 years before Saban arrived, Alabama was not a great program. There were 3 seasons in which we won 10 games. But there were also 4 seasons with losing records, including Mike DuBose taking us to 3-8 in 2000 and 4-7 in 1997.
Michigan, on the otherhand, in the 10 years prior to Harbaugh had only 2 losing seasons. They also had 2 seasons where they went 11-2.
The records for the two teams in the 10 years prior to the arrival of the current coach do not agree with your claim that Bama was a great program and Michigan was a shitty one.
1997 to 2006 Alabama had a W/L record of 67-55.
2005 to 2014 Michigan had a W/L record of 73-53
It took Harbaugh 7 years to get to the playoffs, and didn't get to the championship.
It took Saban 3 years to win a National Championship.\
I think it just seems like Bama was great before Saban, because we have been near the top for so long.