You should still get plenty of airflow through the carburettor even with icing, as the propeller is still windmilling (unless you're much slower than typical gliding speed).
Even thirty seconds of warm air should melt enough ice to allow rough running, I would imagine.
I agree that closing the throttle altogether might be counterproductive. I have started teaching my students that they should leave the throttle partly open until shutdown checks, mainly so they will be able to detect a restart if it happens! (However this is mainly applicable to practising forced landings - not enough time to fool around in an EFATO.)
O8
