I'm also severely emetophobic, and I had my gallbladder removed a few weeks ago.
I was terrified of sickness as I haven't had a GA since I was 12 (I'm 45 now). I posted at the time under another username - try searching for a thread called something like "GA next week - terrified" (I can't remember what it was called, sorry, but I got loads of reassuring responses).
I asked for as many anti emetics as they could give me - apparently you get them in the cocktail of drugs as standard anyway - and no opioids, just IV paracetamol.
Anaesthetist blustered a bit and gave me a lecture about my priorities, but he was good to his word and did what I asked!
However. Upon opening my eyes, they asked me if I felt sick and I said yes (I didn't, not particularly, I was just scared). There was a muted debate behind me about what I'd already had, and the anaesthetist agreed that I could have another of the anti-emetics in their armoury. I don't think I genuinely felt sick - I was just so anxious NOT to that I thought I did!
Regrettably, as a result they gave me a big hit of cyclazine (sp?) - and I reacted rather badly to it, only in the sense that it drained me of all energy and sensation and I couldn't even move my limbs. Apparently it's a cheap anti emetic and a reaction like that is quite common.
I won't lie and said I didn't feel sick at all - I did, but it was quite mild (like feeling travel sick), manageable with sips of cold water and some deep breathing and to be honest, had I been left alone to sleep I would have been fine.
By far the worst part of the thing was feeling so awfully weak and groggy, but that was the post-GA drug and not a direct effect of the anaesthetic itself.
I was frightened at the time and getting over the cyclazine was awful, but I would do it again and next time I won't be quite so quick to say I feel sick upon waking!
From an emetophobe's perspective - the nurse brought me the dreaded emesis bowl as I looked pretty grim, but actually I didn't even care - I just wanted to be left alone, I would vomit in private if it came to that. And I'm a hardcore phobic, trust me.
I wasn't sick. 