Hi Isaac.evans. As dramamama601 said, it's usually okay. I would recommend that you call the theatre directly, and inquire, as each theatre has different rules, and each is open is various interpretations. For example, at the Gershwin, their policy is as follows:
Bag Checks:
All bags will be inspected upon arrival. Luggage, shopping bags and other large packages that will not fit comfortably with you at your seat will not be checked or allowed inside the theatre. For your convenience, please make other arrangements for these items before arriving.
I don't blame you for not wanting to cart your bag around the city. I believe I saw a similar thread recently, and storage places were suggested.
Enjoy your visit!