You can use the GC anywhere the KTTW card is accepted.
However, note that you are better off not using it for dining as typically the preauth for 20-25% more than the total to cover the tips. The unused amounts get held back for a few days.
Best is to charge everything to your KTTW card, and ON THE DAY BEFORE checkout, apply the GC to your room account. The rest will be charged to your credit card the NIGHT BEFORE checkout.