Much as it's a nice narrative if it does work, I'm not sure understanding the club is really all that important. Busby literally spent his career playing for our main rivals and Fergie didn't exactly have a strong connection for the most part before joining. Indeed, if anything, instead of coming in with an understanding of what United was/is, both men instead reshaped that definition due to how good they were, and due to the fact that they were visionaries.
Most fans would (generally speaking) have a strong understanding of the club but they obviously wouldn't have the managerial chops to run it.
You dont have to play for the club to understand what the club is truly about and to know how to convey this. I wouldnt say Fergie did anything to stray far from what our history was known for. He had the same principles as Busby did. He built the club off youth, introduced his own principles and professionalism of course, but also always knew that a big club had to act like a big club and always play to win. Busby played for and captained our greatest rivals, but as much as some might not like to admit it, they're built on pretty much the same principles as we are.
You have to understand what the club is truly about. Its 100%relevant. Mourinho is a great manager and a winner and whatever else. He was never suited to this club. You have to have the respect of the players, but you also have to know the club and even more importantly be able to properly convey that to the players. Solskjaer himself doesnt have to be this great tactician to work out here. But if he has the right attitude and always gives the players the right mentality, to play the United way, while also being able to delegate and not being too proud to take the opinion of others, than there is no reason why it cant work. First thing he did was bring in Sir Alex's #2. He has excellent coaches all around him who all know the club and can transfer that knowledge and attitude to the players.
The biggest thing that Solskjaer has to prove, at least in the short term, is being able to overcome adversity. Nobody wins every game. We'll get a run of bad form. It's important that he then doesnt stray from his and our principles and we keep plugging away instead of ripping it all up and doing dramatic changes like so many managers do.