Hi,
The most difficult part would be the actual drawing framework. you would likely require scripting custom actions, I don't think it would be feasible with the standard set, you would need to draw on textures, which is the main area where custom actions would be required.
as far as the logic, multi player management and various features, playmaker would do very well indeed to let you organize everything logically.
multi player: photon networking system is soon to be released for playmaker, it's currently in beta, so that would be much easier than using Unity networking to start with ( because of the magical photon cloud server, it's all much easier).
I don't have much time at the moment, but if you are one day getting on with this, I would be happy to help you out with the custom actions for drawing onto textures.
Bye,
Jean