Well, unfortunately, the answer seems to be no.
I can add a set of brightmaps for the player default skin and that works.
If, however, I create a set of brightmaps and allocate them to a skin's sprite names, changing to that skin in game does not result in the player's new appearance being brightmapped.
At least what I feared might happen doesn't. I was worried that changing to the new skin would result in the brightmaps allocated to the PLAY* sprites also being allocated to the new skin but, no, the skin simply doesn't use any brightmaps.
I wonder, if the system is already semi skin-sprite aware, would it take much to enable brightmaps for skins?
There are a few places where I wanted to use "scripted marines" with changed skins and I also wanted to use them in botmatches. In both cases, I can currently have any marine or bot that is using the base skin brightmapped but any actors not using them will be quite dull looking in comparison.

Of course, for the former I could include the skin images as proper sprites and just clone the scripted marines...
Even if it's not an easy job, just for the sake of me knowing, would someone mind giving me an idea of how the engine regards skin sprites? By the way they are placed and defined in a WAD and from the brightmaps experiment above, it seems that skin sprites are not really following the rules that are normally associated with sprites. So does the engine see them as a special case only to be used in certain circumstances or something? Do they have their own namespace rather than being sprites? (Also, am I right in saying that the skin format is basically an import from Legacy?)