Surely our own travails under two managers who were both regarded as 'elite' until they came here and didn't succeed is proof enough that we should not.
An 'elite' manager is just a manager who is currently winning or has recently won big trophies with a big club. Mourinho was still regarded as an elite manager when he came to us, and then he failed to live up to that reputation, and was no longer regarded as an elite manager. Before PSG, Tuchel was not yet regarded as an elite manager. Then he went to PSG and (some would argue inevitably, given the league) won some big trophies, and now he's 'elite'. If Solskjaer wins the league with us next season, he will probably then be regarded as an elite manager too. It's a descriptive category, not an actual inherent quality.