This seems pretty easy to test rather than survey... I can pull up Marriott right now and book an award reservation in Dallas for tonight. Are you thinking that there is some point (after checkin time, midnight, etc) where suddenly the award inventory will go away?
Or are you wondering how long it takes the reservation to "show up" at the local hotel so you can check in?
The only time I have ever had problems booking an award was with Hyatt. I was at LAX at 1:00 am, where the Hyatt app/website (and even the Gold Passport desk) wasn't able to access
any inventory, even paid inventory, for "yesterday". It required a call directly to the hotel front desk.
But other than bizarre corner cases like that, I am not aware of any chain that cuts off award inventory for reasons of being "close in" rather than capacity/inventory issues that could occur at any time. Airlines? Yes. Hotels? I would be very surprised to find a hotel with this policy.