When I knocked down my cat myself (he was excited to see me arrive home and ran straight out infront of me and I didn't see him) I had to rush him to the vets and it was much the same as what has happened with Sooty, the vet managed to fix him up pretty well, and the vet was really helpful. He was in a bad way and I was feeding him custard off my hand for three days in the vets, The bill was over £2500 but Fraggle wasn't insured and there was no way that we could have found that kind of money, the vet halved the bill for us as that was really all we had at the time - we had just moved in together and were really stretched financially.
We were very very grateful to them for there help and I'm sure that no vet worth their salt would ever let your animal suffer because of the money issue.
If your insurance said that it was ok to claim after a certain date then I would of thought that it will be fine, stay calm and concentrate on getting your little kitty home!