I really can't answer that either way. I've bought all of my used except for one .375 H&H. And that one I didn't own very long... AAMoF, I didn't even know it was a Custom Shop gun until just before I sold it. It was a std sporterweight. And way too light for that kind of power...
They have a list of options about as long as your arm, so I wouldn't be surprised if it may be bedded right from the factory.
Altho' "Custom Shop" is really a misnomer... A true Custom Shop should make you anything you want. And you can get anything you want from Remingtons ... As long as it's something they offer.
But if you want something they don't offer, your pleas will fall on deaf ears!
In recent years I have seen guns for sale on Gunbroker that had the words:
Custom Shop noted on the barrel. I own nine 40-X's, four Custom Shop Mod: Sevens, and C-Grades in: .243 Win, .280 Rem, and .375 H&H. And none of them have "Custom Shop" noted on the barrel. Some day, I'd like to visit Remington and take a tour of the "Custom Shop"... (If it's possible...)
GH