As stated in the FAQs sticky above
How do I use the 4 annual confirmed suite upgrades for Diamonds?
These confirmed upgrades can only be used in conjunction with a revenue stay (most rates bookable directly with Hyatt qualify). Each of the confirmed upgrades may be applied to stays up to 7 days. These upgrades may only be booked for the “entry suites” as defined at the properties. Booking can only be done by calling a Diamond CSR. There are 4 properties that do not participate in these confirmed suite upgrades: Park Hyatt Beaver Creek, Park Hyatt Sydney, Hyatt Regency Kyoto, Hyatt Regency Paris Madeleine.
Some clarification since you are inquiring about the usage with pre-paid rates: Yes that rate is an "eligible" rate for upgrade - it's better that you call and inquire about the application and book at the same time since the inventory may not be available and you can postpone booking (and paying) for the stay - rates may fluctuate but tends to rise as the hotel fills up.