They all should work, you are buying a regular room with real dollars through a travel agency and then getting a 4% per dollar spent credit fro Barclays. You can pick from a multiple of discounted rates and standard rates.
This actually seems perfect for Hyatt, because they don't have a credit card program. SPG hotels don't count reward stays toward status, so the travelocity card will help there as well.
For me the best is I have "points or dollars" at a better rate, for any hotel or airline.
I'm relatively sure you will NOT receive hotel points/qualifying nights for stays booked on Travelocity. Most hotel chains don't like you booking anywhere except their own site. I would love to be proven wrong though.
For airfare, it will likely be treated just as any other purchased airfare, so I plan on concentrating my redemption on air travel awards.