I can already picture the outrage when one of the big teams have a goal that was onside given as offside on the field of play and it was a close onside so the referees decision is stuck with. Imagine one players shoulder is a close onside in one incident and in another incident another players foot is a close offside but the first was given offside and the latter onside on-field - you will get calls of corruption - especially if it happens to benefit a Man City or Liverpool.
Mostly no, in part because I don’t like some of the hype around the PL and the (perceived by me) as disrespect towards other leagues although that is probably more a social media/broadcaster thing than matchgoing fans in fairness.
As well as that not really liking the sides outside of my own (Chelsea) that often make the Champions League.
I’d probably have to actively have a soft spot for the English side or really dislike the non-Prem side to be cheering on the English team outside of Chelsea.