Well as a Barca's fan i'd say no because it may be better for us if he stayed.
But,trying to be as objective as i can i think Pellegrini isn't completely guilty for Real's terrible performances.
First,this disaster against Alcorcon can't be his fault,players like Raul,Benzema,Guti,Drenthe and co. should have played decently even without a coach ,it's team from Segunda B and i think coach can't help much if players can't do anything to not be humiliated like this.
But also,generally,Pellegrini's era in RM is not something i was entranced by.I understand these are new players,new system,but those are not kids who are playing football for the 1st time.So they had to start a bit better but,more important ,in my opinion is-I always said that good forward doesn't mean winning a treble.Spending so much money to buy CR,Kaka,Benzema... isn't normal when you have such a terrible defense.And now it's becoming obvious how terrible Madrid's actions were during the transfer period.
So now it's actually all same to me ,i think Real can bring 100 new coaches but until January they can't do anything important,till they buy some decent defense players.