What will be interesting to watch is if jersey sales diminish.
I'm not sure if I'd buy another jersey if we got sleeve advertising- it's one thing for the front of the shirt to have a brand associated with the club, but sleeves become a walking billboard.
It's also a bit disingenuous for the PL to do it since they're flush with TV cash, whereas other smaller leagues (Central American) that do it because their very survival is at stake (not that I'd buy their jerseys either, but I understand their positions).
It depends. I'm fairly sure that at the very least a high proportion, if not an overwhelming majority, of shirt sales come from parents buying shirts for their kids or from tourists at games/casual fans to whom an extra sponsor is irrelevant because they are buying into the fandom of a "world club". The percentage of fans who will be so incensed as to now refuse to buy the shirts are pretty small, especially considering they will almost certainly form only a minority out of that minority who aren't of the first two groups.
Also bear in mind that the takings from shirt sales are pretty low, even for some of the world's top clubs. The reasons that kit manufacturers are now willing to sponsor teams almost more than the shirt sponsors, even though their logos are smaller and therefore get less exposure on TV, is because they take the lion's share of all shirt sales. Of all the teams in the world, as of the latest figures I saw (approx. 2015) only about two or three teams sold more than a million each. The rest of the PL's "Big Five" clubs only sell between about 800k down to City decidedly bringing up the rear with barely 300k, which means they aren't even in the top 20 clubs worldwide for shirt sales - even the likes of Galatasaray and Olympique Marseille sell more.
From those figures, clubs make barely £10 a shirt, and perhaps even half of that, because the kit manufacturer swallows most of the profit and then because most clubs contract out to companies like KitBag to handle their sales too. That means that City are probably making at most £3m from shirt sales a year, and possibly closer to £1m. (This, incidentally, is why you should laugh with derision whenever anyone claims that if a club ever signed Messi then they'd make the transfer fee back in shirt sales).
When you bring that figure back to my first paragraph, where I doubt that clubs will really lose that many sales because of this, then you realise that their potential loss from this may be as low as £100,000, and likely isn't any higher than £500,000. I guarantee that the yearly takings from this new form of sponsorship is a whole lot higher than that.