Yes. Though the YJ-83K doesn't seem to have much of a long range compared to other mainline AShMs in the PLA arsenal, and is both non-LO and subsonic. So I'd suppose that such loadouts on a H-6 would be used for the finishing-off segment of anti-ship missions?
I am hesitant if the rotary launcher described is intended for H-6K family's internal weapons bay to begin with; from a horizontal footprint and depth perspective in particular. For all we know it may just be work done as part of gaining experience rather than for a specific project, and just recognizing that an internal rotary launcher in general is useful for a strategic bomber (whether H-20 or otherwise).
That said, if it is compatible with H-6K's bomb bay from a footprint perspective, I suspect the missiles themselves would not be a direct YJ-83K family. Given what we know most payloads on internal rotary launchers look like, their folded physical footprints tend to be quite streamlined and low profile, which YJ-83K is not (even if it was a folded mid-wing version).
If this was to be implemented in practice they might have to develop a whole new missile for it.
CJ-20 is basically the air-launched variant of CJ-10.
The nomenclature is a bit confusing, because "CJ" is sometimes used interchangeably with the "DF" prefix, for a ground launched weapon.
DF/CJ-10, DF/CJ-100, DF/CJ-1000 are three different weapons with CJ/DF prefixes.
I am not sure if CJ-20 is an actual designation -- my understanding is KD-20 is the air launched version of DF/CJ-10, but that CJ-20 isn't used for the air launched version.