Just how well any tape would hold up in the copying process is a question you'd have to ask the guy doing the work. Also when removing the tape, (if it is a way to protect the finish), may do more damage by pulling finish off with the tape.
The follower stylus on the duplicator could be adjusted the few .000" to allow for the thickness that's been added to the outside surfaces by the tape. But it's the avoidance of scratches that's the main goal. The few extra .000" of wood will disappear in the finishing. I've had Mike do a few stocks for me and I always tell him to allow a bit extra on the outside anyway.
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http://www.gunstockduplicating.com/>
Give him a call and see what he says about the idea.