No, there are no "Dreams" being issued during the party, but you will see "Magical Moments". The offical rules state that Dreams are being issued until 5pm (but Disney has the right to grant them later if say the the person that is getting the Castle stay can't accept but it's already 4pm, they can put the prize back in the mix to be reassigned at a new time and location). Dreams would be any of the physical prizes, hats, fastpasses, trips, anything that is listed in the official rules of the sweepstakes. Magical Moments are events that happen in and around the parks that create a moment for you but are not offical sweepstakes prizes. (for example, the 30th person in line for ice cream gets theirs free, or riding in the wheelhouse on the Riverboat, etc)
The Dream Squad has two roles, there is the Prize Team and Super Greeters. The Prize Team wears a white vest with the logo on the back and will be issuing the prizes throughout the day. The Super Greeters are basically assigned to a section of the park and they mix and mingle. They are there to answer questions, assist you with anything you might need, help out the other cast with making sure the area is presentable...the Super Greeter is there to make sure that everyone is having a great time. These Cast members are inthe park from open until close so you will see them at the parties, but they do not have "Dreams" (official sweepstakes prizes) to give out.