With only the scraps we have now, any statements about D&D 4e are purely speculative.
However, for me a "generic" system is one a GM can tinker with and customize for just about any genre. Some, like GURPS and Hero, give you tools to synthesize any ability you need; others, like BRP and especially PDQ, have such a simple foundation that a GM can add whatever he or she needs.
D&D has never really been either of those things. Creating new classes (and now feats) has always been a black art, requiring rigorous playtesting to avoid PCs who are either wimps or gods. D&D itself also makes certain assumptions: PCs fall into discrete classes, magic works in a specific way (or three specific ways: arcane, divine, psionic), etc.
Maybe the promised Modern system will provide more flexibility, but I doubt the upcoming D&D will encompass anything but, well, D&D.
"On two occasions I have been asked [by members of Parliament], 'Pray, Mr. Babbage, if you put into the machine wrong figures, will the right answers come out?' I am not able rightly to apprehend the kind of confusion of ideas that could provoke such a question."
- Charles Babbage (1791 - 1871)