Color at Vertices (CAV)
The short answer to the question is No. Well, if we are to be perfectly honest the elongated answer is sadly no as well. At least not in any sense that can be even remotely considered a 3d painting feature. With that being said, you do have some basic options to paint or store (color) information directly on your geometry. While they are limited at best, yet they just might do the trick if you’re not in the need of anything too fancy.
From the Get > Primitive > Polygon Mesh menu, chose Grid and increase the U and V Subdivisions to 24 or so. To get a bit more points to work with as well as to smoothen the result, press [+] to subdivide the grid. With the grid still selected, chose Get > Property > Color at Vertices Map. From the Get > Property > Map Paint Tools menu chose Paint Vertex Color Tool, shortcut [Shift] + [W] to activate the paint tool. Next, from the Get > Property menu chose Brush Properties… (shortcut [Ctrl] + [W]) and switch to the Vertex Colors tab in the PPG. This is where you customize your brush as well as changing what color to paint with etc. While you naturally can colorize your geometry at this stage, an alternative is to paint a matte instead. Set the color to black and paint something on the grid. Change the color to white and paint something else.
From the Get > Material menu chose Blinn and press  to open a Render Tree. From the Nodes > Mixers get a Mix 2 Colors node and from Nodes > Map Lookups get a Vertex RGBA Lookup node. Connect the Vertex RGBA node to the Weight input of the Mix 2 Colors node and the Mix 2 Colors node to the Ambient and Diffuse input of the Blinn node. Since you’re using a mixer you have the option to ether set the colors in the Mix 2 colors PPG or taking it even further by using textures instead. If you choose to colorize the geometry rather than creating the matte, simply connect the Vertex RGBA node directly to the Blinn and you’re done.
Though it’s far from being a 3d paint solution, the Color at Vertices (CAV) maps can still be of great useChange the Color Paint Mode to Smooth and paint over the different colored areas to blend them together.
Use the CAV maps to paint mattes rather than to colorize the geometry, as you’ll then have the option to use any mixture of colors and textures in the Render Tree.