While it may be possible to push some grit into the chains while wiping it down, that's going to be hard. After all, the pins are press fit (and then riveted on modern chains).

But the point of wiping a chain, as I see it, is to get most of the exterior oil off. That oil standing on the outside of a chain will collect dirt, dust, and road grit. To the extent you can keep that from sitting on the outside of the chain, the chances of it working its way inside the chain (as the plates rotate going around a sprocket/cog/idler pulley and then straightening) are reduced.

My take on the question? Wipe it down until there's the thinnest film left as a rust preservative on the surface. It should be so thin that the gunk is too heavy for the oil to hold It there. After a re-lube, wipe side plates, wipe the rollers while forcing the chain to bend so you rotate the rollers. Then go for a ride or four, and repeat the wiping routine. Forget about it until the chain starts squeaking.