Personally I just use my lightning address and don't use a primal address at all (which admittedly is less convenient when I am happening to be using primal, but I really just didn't want another kyc place to hold bitcoin). You absolutely could do this by adding your @strike address to your profile as your lightning address. Not 100% sure what'll happen with the primal wallet though -- it'll still be there, and I would mostly expect that all zaps should go to your strike address, but I'm curious if you may run into weirdness from people also using primal.