My vet lives down the road from the yard, so will normally drop them off on the way past anyway, and quite often will just nip in to make sure he believs me!!
Don't think they're supposed to, but my old vet used to give bute to me for my arthritic horse whenever I ran out without seeing him. But the vet knew me and the horse very well.
If you have a good relationship with your vet then yes I'd imagine most will give it to you. My vet in the UK always gave me extra to keep incase I needed it for any horses.
Over here I have large tubs of it; I have 4 tubs at the moment. It's very cheap and obviously because I have so many horses, I do need to keep stocks of a number of veterinary drugs here incase of emergencies.
My vet will for Cairo and has sent me bute on several occasions over the years.
Cairo is now on danilon and it looks as though it now be long term/rest of his days due to a lot of old age joint pains. He gives me prescriptions so I can get it from the web where it is a lot cheaper. He sees Cairo every six months as a matter of course, he and Chancer are six months apart on their jabs, plus Cairo's eye is checked for cancer twice a year.
I think my vet would give me some for Chancer, as he knows that if it was more than say a kick needing some pain treatment for a couple of days, I would have him out in any case to check him.
As long as the vets know you well and you tell them what you need it for then they often will. I get as much bute as I like as one of mine has athritis so I can use it for others if I have to as well.