Arelith

I've gotten different answers from different people so I figured I'd just get a compilation here and take the most supported one:

Does the shadow dancer class add to shadowmage CL vs dispels?

If yes, is it only with the shadow out?

Shadowmage is a popular class right? It means the wiki is likely correct. And the wiki sounds quite conclusive that SD lvls count as full caster levels and there's no mention of the shadow there. Do you have any reason to suspect it's incorrect?
EDIT: apology, I do see a mention of the shadow now, but it doesnt need to be out. It would need to be out for the sneak bonus the SM doesnt get.

SD adds to SM CL for spells and dispels. It does not require the shadow, it also does not offer any extra spells known/spell per day.