I'm also emetophobic.
I can't clean up my own puke because after it happens I feel far too faint and wobbly to do anything.
But then I almost always make it to the toilet, the rare couple of times I've been too ill to get to the toilet I have had a bucket at the ready. So cleaning up is simply a matter of emptying and disinfecting the bucket. I last puked on the floor aged around 5, I was in the top bunk, and wasn't allowed to get up by myself in the night!
If DH is ill, I am to be found outside (in just a pair of pants once) or huddled in a corner somewhere. I physically can't clean up after him, I tried once when he just missed the toilet but when I saw it/smelt it through the open bathroom door my legs gave way and I fell down the stairs.
Thankfully, DH is starting (after 10 or so years) to come round to my way of thinking, if you're unsure then it's far better to have a bucket and not need it, than to need a bucket and not have one! And I was so proud of myself last time he was ill, he emptied the bucket himself and went back to bed, and I did the disinfecting of the bucket.
Anyway, for whoever asked, yes I would leave vomit all over the bedroom, if DH couldn't clean it up then I would have to leave it. I'd also not use the bedroom till at a minimum it had been professionally cleaned, the smell had cleared and if there were any lingering stains/smells, it would need to be redecorated!