I don't know about shooting on one foot - shooting from awkward positions makes sense (I dabble in USPSA, and practicing transitions and draws, and shooting around obstacles sounds pretty similar.)
Now, w. the Pup... The gun is accurate, but I don't know that there's really enough of a grip to it to worry all that much about precise shooting. IMO, its best use is so close up that you can't miss, and there's no point in using sights.
I would think the best things to practice w. the pup would be very close quarter shooting, shooting from retention, etc.
If nothing else, I just don't see how anyone, aside from a handful of the really gifted, would ever be able to obtain a good enough sight picture to use it much beyond 7 yards.
Maybe get an OWB holster for it, and shoot it in some IDPA stages - I don't think a whole match would really be feasible, unless they were all v. short distances, but some stages would work.