Yes I have experience with this, although not as extreme as your situation.

My almost 2 year old had separation anxiety when starting here, and would meltdown completely during lunch. Child cried so hard, would spit up/vomit at the table. Luckily never a large amount and always onto a plastic bib. I learned to anticipate it and be standing by so I can clean it up quickly.
Although I have a policy regarding vomiting, I never sent child home as I was confident it wasn't due to illness, just intense crying and anxiety. But I would always keep mom informed as it happened, indicating I may ask for pickup if necessary.
As the child adjusted to daycare it happened less and less. I think it was only a couple of weeks before it stopped and hasn't done so since which was a huge relief!
How long has this been going on for you?

My situation turned out ok but not sure I would have been able to continue if it went on longer.