While I certainly don't expect them to give out promo codes willy nilly, my recent experience is that they've actively tried to get me to spend as much as possible on a given set of tickets. At the Walter Kerr, when I said I had a code they didn't ask for it, and just applied one with a much smaller discount (until I realized, and said something). At the Lyceum, they tried to push me to buy pricier seats to the point where I almost felt swindled.
Of course, this is just anecdotal. Whether they felt some obligation to the producers, arbitrary spite towards me, or something else, I don't know.