The check certificates do get full stay credit. The ones that they sell are $50 each certificate. You can buy them at face value from Hyatt, or they have the ones sold at the US Costco for 20% off.

You may run into some currency conversion problems outside the US. Often the hotel conversion rate is pretty bad, so this will weaken your discount. In Indonesia this year, I was taking over a 10% hit, but they agreed that if the bill was all paid in dollars (and nothing converted into local currency), then I would just pay the bill as it was booked. (Room booked in USD).