The OP wasn't specific about whether they wanted to use a 6.5X47L bushing die to neck down 6.5 cases to 6mm or to resize 6X47L fired cases for reloading. Since we don't know for sure, let's assume both.
Can a bushing die be used to neck down cases? Yes, I've done it many times, but IMHO it's a total PITA. A bushing die most often doesn't resize the neck all the way to the shoulder, can result in deformed and misaligned necks and usually takes several steps. Obviously, using Peterson 6X47L brass solves the necking down problem, but does nothing to answer the question about resizing after firing. Although I have a Whidden 6X47L FL bushing die, I have always used a 6X47L Forster FL (non-bushing) die to neck down 6.5 Lapua brass. At first I used a Redding 6X47L body die as an intermediate step to reduce the neck diameter, but lately I just neck down in one step with the Forster die. Works perfectly.
I can then resize fired brass using either the Forster or Whidden dies. I usually choose the Forster die since it seems to fit my chamber a bit better. I ordered a separate .224 decapping rod and expander ball with the Whidden die and most often use it to load 22X47L.