finnie don't know about Glasgow dvla but i've done 2 recently over at edinburgh.
Just seems to be pot luck depending on how busy they are - first one they were really busy (end of month!) so took all the docs and sent out about a weekish later.
Second one, nice and quiet, they got me to run out and get my tax disc and gave me new tax disc and mot there and then - so could get plate straight onto car
still waiting on v5 a month later tho!
Insurance is not a problem either way, just give em a call with new reg no. mine didn't even charge for the change.
Dunno if it'll be different tho if you've gotta tax the car as well when you're there - i'd give em a call.