it’s really gonna depend a lot on the wood. For example, the pre-finished proofgrade wicks way less than unfinished baltic birch. The oil pens certainly seem to wick less than water or alcohol based ones. Wax/solid paint markers don’t wick, but they have their own issues.
I also wouldn’t be surprised if some of the more resinous woods might self-seal to an extent, from the heat of cutting/engraving, but that’s just a guess.