Can you use it in shops, restaurants, to pay a room-only reservation balance, upgrade or purchase tickets, and to make payments on your room charge account? Absolutely - in the same way anyone would use a regular credit card.
Can you use it as the credit card on file to back up your room charge account when you check in? Depends. In most cases, yes, but some debit systems do not allow for "opening tabs" or placing holds. For this, you'll need to check the fine print and/or contact customer service for the card.
Can you use it at an ATM to get cash? Of course, but then the fees kick in - which are quite high unless you are using a Chase debit card (all of the ATMs on property belong to Chase so are free to Chase accountholders).