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Sorry, I don't fly a 737 but I can tell you it's common to turn off packs, engine and apu bleeds whilst being squirted with glycol etc.
Usually this "silence" would continue for about a minute after the de-icing was finished to ensure the fluid had dissipated around the engine cowls.
Typically, the taxi checklist (and control surface check) is repeated again and this is where the bleeds are usually returned to their desired operational position.
The de-icer's do their level best not to spray in to the engines but sometimes the wind/conditions make this an impossibility.
Hope this helps.
Cheers,dd.