Yes I believe all daily passes are valid on the "Airlink" service ... however if you're parking at the Carlton you'd need to get a shuttle bus back to the airport to catch the airlink (you can catch the regular 41 bus from accross the road into town - though it's not so frequent and slower than the airlink)
Unless there's a particular reason for parking at the Carlton you might consider driving closer into town where there's more frequent buses and a shorter journey time into town