THAT actually is what I was asking. People are shopping in NYC all the time. Didn't know if you were even allowed to take bags to your seat or if you had to "check" them and get a claim ticket to retrieve after the show. No big deal.
Ah. No, there's no theatre I know of has any sortof bag (or coat) check. Many of our theatres are like 100 years old. There's noplace it'd be feasible for 1000 people or whatever a house is, even just coats. The space just doesn't exist.
It's not a thing in larger, newer theatres either here though, come to think of it. Lincoln Center you sit on your coat and stuff a bag under your seat (there may exist a coat check in the basement someplace I have some vague idea but it's not really a used thing if it does exist).