From what I can remember my impressions were initially used to map out the length of wire needed and the number of brackets etc and generally to get a feel and a quick reference guide for the orthodontist.
I certainly don't remember having "after" impressions taken, only before. I think they're probably also quite good for designing retainers.
I know your pain with the impressions. I don't mind dental stuff but orthodontics I really didn't enjoy. I didn't really like my orthodontist I found him really annoying actually lol and the impressions really tickled my gag reflex and I hated the taste. So I know your pain. I can empathise... but I don't know whether you absolutely HAVE to have an impression taken? I'd ask your orthodontist and see if you can avoid it if you're really worried about gagging, choking or indeed puking. I wasn't initially worried but I can say I wouldn't want to have one again given the choice.