First I would check to see what the barrel manufacturer has to say about barrel break-in, then I'd ask the smith that mounted it for me what he thought about what the manufacturer said. There's more than a few that feel break-in is a waste, especially on a custom barrel.
I have had a couple nationally known smiths tell me that I should do it if I felt it would make me more confident in the barrel, but that the barrel really didn't need it.