Honestly I would be pretty shocked if anyone except the front desk staff at the Cosmo would know to process a Marriott Gift Card. The restaurants know how to charge it to a room account which you can then pay with the gift card, but I don't think you'll be able to do what you want without staying there.

I mean you can try, but I'd go in assuming it won't work and I'd have to pay by other means and if the gift card works it'd be a happy surprise.

Have you been calling the hotel or the restaurants? I'd try calling STK or whatever restaurant it is you're interested in and asking them.