They would not have coat check at this time of year.
I can't think of any location in the theatre where you could have a piece of luggage by your seat without blocking the aisles.
Additionally, given the procedure to inspect bags, you would have to open the suitcase and allow staff to fully check it before entering, so I would recommend against taking anything large.
This week, particularly. I imagine that venues will be less likely to want those types of things around (Broadway Bares has banned bags, just like sports stadiums), let alone when you would / could walk away from it.
While it is wonderful that you want to get in one last show, perhaps it is better to skip the theatre,