I doubt it. I'll scale down the NYPD to 1/8 of it's size so it's 4,000 people. American police departments have pretty extensive weaponry that they get from the DoD & Homeland Security. I'd bet on 4,000 cops using the armory of a modern police force over 100,000 Mongols.

Then of course, you have to deal with weapons held by the local populace, logistical concerns (cars, elevators), and other potential advantages like poison for horses.

As said already, police plus an armed populace would make short work of them in all likelihood. Not to mention modern cities are far more densely populated and harder to navigate on horseback compared to what the Mongols were used to.