No, because packages have to be paid for in full prior to arrival. The GC isn't given until check in.
The only way someone can use the GC that is being offered now to pay for the room would be to book the first 5 nights of a trip as a package to get the gift card and then book the rest of the trip as "room only". Then the GC can be used to pay for those other nights as room only ressies get paid when you are there.