Sure it's possible to paint the terrain. In T3D, there really is no difference between "play mode" and "edit mode". It's the same mode, just different UI.
However, I would have to question whether it is the best solution to whatever you are trying to achieve.
As Duion mentioned, it's really resource intensive and the terrain is not designed to be repainted during play. If you are doing a singleplayer-only game it is definetly not too big of a task to implement however.
You should consider whether decals is the better solution to your problem however, as it is networked, more efficient and allows for a higher level of detail.