No, no caulk. The deck boards are going to shrink significantly, which will pull the caulk away from the house. Before redecking, flashing should be installed on the ledger board (framework board against the house) under the new deck boards. Pre-shaped flashing is available where ever you purchase your new deck boards.
There is a good possibility that there already IS flashing installed. If it is there, there is no need to replace.
Will you be using pressure treated 5/4 decking?
