It's definitely hotel-dependent. For example, I had the HH in San Diego charge me the 1 night as a deposit on a refundable rate, which despite being in the terms is rarely enforced by most Hyatt hotels I've booked on refundable rates.

I recently booked the Mar Monte (Unbound) for a stay next month. Booked the member advance purchase rate to use an amex offer that was expiring today. Advance payment was charged the next day as expected.