R.J.
You don't need to drain it.
Vinyl Cement & vinyl patches bond and work under water. The pool should have come with a little patching kit, and at any pool store you can buy the big patches and big ole' bottle of vinyl cement. ((We have a lab that likes to jump in out 15'x4' Intex Pool... we've patched it many times)).
That said... the 3 most common causes for leaks aren't holes... and we've had to deal with both many many times:
1) The ring isn't fully inflated (it should be balloon full... less than and it will sag and the water will runeth out.
2) One of the holes in the pool (either the filter or the drain holes) is leaking. The drain hole just needs to be plugged. If it's from the filter holes... you pressure seal them off... and rescrew them back in. ((We upgraded our filter and had to cut bigger holes for it... vinyl cement also works there... poured over like honey... it stops the leaks mid flow)).
3) Slight unevenness of the ground. If it's tilted at all, and the water is touching the ring at all, the ring can fold down draining out hundreds of gallons.