No, you don't receive any credit at all. Your package is completely independent of the GAD promotion.
If you want to take advantage of the free 1-day base ticket for the GAD promotion, you need to book WITHOUT tickets, and then when you arrive and go to a park the first time, go to a ticket booth (most likely the will-call booth), turn in the voucher you will have received for the GAD ticket, and then upgrade it to the ticket you require.
Or keep your package, and either pocket the tickets that came with it for a later trip and use the GAD ticket as above, or use the package tickets and opt for one of the other GAD options (Fastpass exchange card, souvenir ears and pins, or donate ticket) since you will already have a multi-day ticket.
There are blackout days - I don't have them specifically (they are clearly spelled out in the details), but I believe it was a couple weeks in April, around July 4th, and Dec. 15th was the last day it could be used.