Wipers in the MEL say check landing capability.
However in the air, provided you have rain repellant on the PF side, wipers are not a requirement for cat 2 or 3 (b) approaches.
QRH OPS-OPS-4:
WINDSHIELD WIPERS OR RAIN REPELLENT (if activated)......number required: 1 on PF side
You'd have to return if it wouldn't stop running - that's all there is to it - unless you're one of these believers in the 'grey area' - remember as a pilot you have all of the responsibility and none of the authority - the managers keep that for themselves - That's of course unless all bets are off - this isn't the case here.