they have classes in there but they are all one big section of html we'd have to parse. For instance, unlike Feats, there is no separate item to drag and drop for traits, racial traits, or class features. Plus the compendium is not even done or updated (I've found a number of bugs in the spells alone).
They are going to make an effort to "redo" or cleanup the Pathfinder compendium. I already asked them to split up race and class to have dragable class features. I don't know if it will happen.
Iim thinking of adding parsing for statblocks and text from the SRD as well as compendium someday. but that's a ways off. the sheet is so big and slow and clunky and buggy IDK .