I (very luckily) got my car IVA'd, registered, insured and on the road in a single day this time last year. The IVA was a re-test presented by Caterham Cars, for which they knew what needed to be done to get the pass, it having been the first (I think) amateur built car they presented at IVA. I turned up at the DVLA office in Gillingham with a load of build pictures and all my documents completed accurately and I was in and out in half an hour - 5 minutes at the desk itself.
I'm not suggesting it's always that easy but it can be done, especially if they are no longer requiring separate inspection!
Good luck