While Iturbide was alarmed by the radical liberal movement in Spain, he was also a royalist who believed (correctly, IMO) that the only way to keep a monarchy in New Spain was to have a crown in Mexico, not ruled from afar. While ostensibly he led the overthrow in the name of a Bourbon, I'm not so sure that it had to be a conservative Bourbon (only the youngest had any liberal in him at all, and I don't think he was overwhelmingly so). He was more afraid of the populous masses inducing ultra liberalism on their way to republicanism. Had Ferdinand led the charge toward a more liberal regime (as opposed to having it imposed upon his protesting body), Iturbide might not have been so ready to switch sides. He was concerned about the inmates running the asylum and the effects on New Spain. Plus, part of me suspects that he knew the Bourbons weren't going to accept the crown of New Spain, conveniently leaving himself as a leading candidate for king/Boss. It was a twist on the caudillo head honcho politics that went on elsewhere in the Spanish colonies, but the result was the same: kick out the Spanish crown and takeover as top boss for life, or until another strong man kicks him out.
Had Ferdinand died, and Carlos taken over (presuming Carlos IV doesn't make a bid for return), it's quite possible things go the same in New Spain. Carlos is just as conservative as Ferdinand, and is just as likely to have the liberal masses try running the show, forcing their way to the forefront in the timeframe in question. I don't think switching kings automatically butterflies the events in New Spain.