Turns out the idea has been around for a while.
The mad Brits used to have a "Makita 600 Cordless Challenge" at the Beale Park Boat Show.
A 600m sprint attracting tri hulls, cats as well as monohulls, with multi-engine installations. Inboards, outboards and even paddle wheels - not to mention of course, the inevitable eccentric in a twin-engine cordless drill-powered floating motorbike side car.
You can probably guess the prize
https://www.youtube.com/watch?v=rVrmhoHepmk
(David T I don't know if you are serious, but I can't see the need for any fancy engineering. If there is somewhere on the back of an inflatable to lash to, I would have thought a loose lashing around the rotating shaft would do well enough, of that cheap slippery rope (I forget what its called), you hold the drill in your hand of course. Quick to dismantle should you find you suddenly need to do some home handyman work on your boat. And as for water-proofing - same as for any outboard I suppose - just try not to drop it in the tide.
David Th (very serious) - Ah! But you can't drill a hole in something with a pair of oars can you? Eh? I agree, the last thing we need on a junk is "needless junk", but I reckon in a flat calm one of those little Kohler catamarans should go like a rocket with a couple of 18V Ryobis on the back! (One in reverse of course - counter rotating props LH RH))