!st thing to get damaged will be the rims, a 37 tire will have more air in it.
Hybrids above a minimum price point will have a suspension fork.
add a suspension seat post..
OTOH , there are some small wheel Chubby tires on like folding bikes from
like daHon, to take the bike in off the street, park it in a corner, folded up.
so It won't get damaged or Stolen from the street..
I would bring a bike I wanted to keep , in with me , if I were in NYC.
Bike Friday Tikit, the better of the lot, there is a Green Speed slick
40mm wide tire for those wheel-sizes.