A conference championship is possible as teams with worse average recruiting rankings (i.e. Wisconsin) have managed to win conference titles.
A national championship however is extremely unlikely with the current team, imho. The last 10 national championship teams have recruited an ESPN Top 10 class in the year prior to winning a title. That does not mean this is an absolute qualifier, but it does show the current trend in college football. I do think if Nebraska wants a legitimate shot at winning a national title again then they will have to have a Top 10 class (or really close to it) on the roster when it happens.
I think if you are just looking at that one thing, that is simply a coincidence that happened. No way does a recruiting class have a major impact on winning an NC the next year in football.
I suspect if recruiting is a major factor in winning those championships, if you look 3-5 years prior, their recruiting was a bigger factor than the year just before winning it.
I don't understand how that could be viewed as merely a 'coincidence.' An event that happens a couple times, sure. But, 10 straight years in a row, applying to several teams from different conferences? That's not a coincidence - that's a trend.
Most of the teams that won titles in the previous 10 years also had Top 10 classes in 2-3 years prior to their title, as well.
Again, that does mean this is a championship requirement. But, the current trend suggests that if you want to win a national title you have to recruit at a Top 10 level.