Not if the lock is applied quickly... going down on your free hand is a good way to break your wrist.
When I played with the jujitsu guys, there was no time to think about doing such and such ukemi, and in most cases, you wouldn't even feel a correctly applied technique coming on until you've hit the floor.
'Inspired' (my own interpretation of) by Sensei Amdurs ukemi DVD (apologise for the apparent brown nosing, however, credit where it is due), if you 'follow' (dirty word I know) the technique into jigatai to absorb the initial movement by releasing some of the pressure on the elbow. Then placing the free arm down and make the worm. Seems to work well for me in robust practice (I dont know another way) if shite follows you to the floor then you are no worse off for making this fall. Either way, in the real world, you'll never play the piano again......