I doubt we'll see any current animated dramas in America. For one, most Americans, when they see animation, they will assume it's meant for kids and/or is a comedy rather than a drama. Another reason is the cost of keeping an hour long animation on tv. The best we could do for any animated drama is to get them from other countries, like Japan.
Btw: King of the Hill is the closest to an animated drama, but that's been canceled a few years ago.