Yes, Redrose, that's a (gorgeous!) double rose impatien. What a score for 2 bucks! Most kinds of impatiens re-seed, but I don't know about the double roses. You can root cuttings fairly easy, though. Just stick 'em down in some moist potting soil and don't let 'em get dry.
I agree with the two above, cuttings root easily. If you make sure the cutting has little sprouts beside the leaves (vegetative breaks) you will have a prettier plant. I've not seen the doubles make any seed.