No, a fairweather fan would haven been long gone by december.
I understand what it means to have no choice at all and I respect the difference, but it's not like that if Mourinho is hired for next year I can pick a different PL side and decide to support them. I'm just predicting that I will get annoyed, feel disappointed and my interest will fade. I see what you are trying to do here but as I want the same thing, there's no reason to dismiss my views beforehand.
Still it seems strange to me, not as much as a distant and purely rational viewpoint, but really hoping for a loss during the game? And if those people really were prepared to take one step back to take two forward, they wouldn't want the manager sacked in the first place. So I think it's more about frustration and not liking someone than about proper judgement.
The choice might work out wrong, but at least it's a choice that's the product of a clear vision on the state of the club, squad and how to get back to the top. Mourinho would just be the easy coward way out for a board that has no vision at all and ignores what has changed the last few years.