I don't know about DAP Caulking (seems it is a brand and not a specific product so I couldn't look it up. I'm from Australia so we don't have it here).

Just make sure the filler you use is flexible. A lot of basic caulking dries are and will just rip drywall off or flex the sheet instead of stretching. There are flexible gap fillers that are silicone based which would be better. Bathroom ones are available in white and a mould resistant otherwise there are paintable flexible ones out there too.