I have puked through a regulator before, several years ago just after I was certified. We were diving out of Islamorada and it was a rather rough day. The french toast I had a bit earlier just didn't want to stay down. As we were descending, I felt the urge to vomit. I just kept my reg in my mouth and let it happen. There were no issues, besides the yellow jack with an affinity for french toast. After the ordeal, I switched to my octo (I wasn't Hogarthian at the time!) very briefly to rinse the remnant chunks out of the second stage. My buddy was within an arms reach at all times, and when it was over, he flipped me an OK and we continued the dive. Note that if I was uncomfortable, I would've thumbed the dive, but truthfully I felt great and there was a heck of a lot less wave action on the bottom than on the surface!
Despite this, I still eat before virtually every dive. Calories=Warmth!
Oh, IIRC, the epiglottis is closed while vomitting, so it would behoove you to not ascend while actively vomitting.
Cheers,
Anthony