depends on how you want to paint in 2D....
its entirely doable to directly paint a texture straight onto the object in maya, nearly the same as painting an actual physical sculpture. Effectively what you're doing is actually creating the files that is referenced when the object is rendered. This becomes handy to, say, paint something on a curved surfafce to minimize distortion on the 3D object (such as lettering on a sphere - although there are a number of other ways to deal with this as well). You could also use this method to do 'detail' painting on any number of objects, where the posistion of the faces isn't necessarily readily identifiable inside of a texture map, and where continuity is important.
Note that this only deals with elements for a texture file - color, bump and displacement maps, reflectivity, and so on.

If you want 3D elements (such as the various grass elements and whatelse from the various brushes), I think you're still stuck with defining things from along a curve. Although this could be seen as a slight disadvantage, it does have at least 2 merits that immediately come to mind - you can control its posistion and existence along the curve, and the curve should still be editable, allowing for reanimateable posistions.