I don't think so. There is no option to check on your pokemon in the underground, so I assume you leave them at the door, so to speak. I think this belongs in the General Q and A thread so maybe a mod can move it?
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no cause I had an Eevee egg.....i think.....and I walked around digging up a bunch of stuff, meeting ppl for my Spiritomb, and no dice. The egg status stayed the same