The easy one is this: Comiskey or not, there will be an American League team in the second largest city in the nation at the time (which it was, btw, until rather recently). That's a foregone conclusion.
Now, as to Comiskey the nickel nurser and the Black Sox: Comiskey took it to an extreme, but as a very general rule, owners in that era weren't particularly generous. Parks were smaller, and they pretty much lived and died by the turnstiles unless they had another source or sources of income (e.g., brewing before Prohibition). Thus, it's possible that with the right cast of characters (e.g, Chick Gandil as a ringleader) and the right amount of money waved around, it could happen anyhow. My sense is that without Comiskey's extreme penny-pinching, it would be a lot less likely--but still possible.
I've always wondered why the Sox in 1919 didn't decide to tell the gamblers to go pound sand and win it for themselves--after all, they were heavily favored--and then hold out en masse in early 1920. True, it might be tough to get Eddie Collins to go along since he was actually getting paid what he was worth, but if he did (or at least stood aside), Comiskey is faced with the problem of his entire team refusing to report to spring training without sizable salary increases.
He can then (a) knuckle under; (b) dismantle the team through trades and sales, but then he's likely to have a loser for years to come; (c) sell the franchise. My guess is that he'd chose (b), and he would probably try to exile the key players/ringleaders to the nether regions of the game in a spirit of vindictiveness. Thus, you'd wind up with Eddie Collins playing for (let's say) the St. Louis Browns, Eddie Cicotte with the Boston Braves, and so on.
Should Collins go to the Browns, that might just put them over the top in 1922, the year when the team finished with a winning percentage better than .600 but one in which they missed the pennant by one game. Try this on for size: McGraw's New York Giants losing to the St. Louis Browns in the 1922 Series. That might make the Browns the premier team in St. Louis, and force the Cardinals to move eventually. Perhaps they, rather than the Browns, would move to Baltimore in the late 1940s/early 1950s--or as the Browns tried to do, move to Los Angeles in the early (pre-Pearl Harbor) 1940s?