Most film critics would cite True Dramas that aren't about dialogue, but visuals that provide most of the drama. Terence Malick's Badlands is the first example I would cite. Japan's Mabarosi is a more recent example (but that's Japan, and we know how much animation fans love Japan). Heck, silent films had to make due with very little dialogue, yet had to sell drama.
Using visual dramas such as Badlands as an example, ANY art technique could be used to create drama, including animation.
Of course, Americans don't seem to like live-action visual dramas either. Badlands was an art film, not a box office smash. Why animate a film that no one would watch in live-action? (Waking Life made a bit of an impression, though.)
If you want a dialogue-heavy animated drama, good luck. I have enough problems tolerating such shows from Japan.