Depends how long the wait is. If it's too long without properly backing the manager, then it will affect our performance on the pitch. In fact, even 1 summer window, like we've seen last summer, is enough to put us considerably behind not only City, but also Liverpool, Chelsea and potentially Arsenal given how competitive the league is.
He was backed the first season, 2017 summer he wanted Perisic and Woodward didn't back him and last summer he got 1 first team signing (so 2 short from what he wanted reportedly). So no, I wouldn't say he has been entirely backed. Saying that, if Mourinho wanted experienced players who were close to already being on the decline, then I can see why the board didn't back that. But that should have been made clear months before the transfer window opened so that players who fit what both Mourinho and the board wanted could be targeted. A DOF could well be the solution for that but that discussion is for another thread.