You can paint anywhere but to set a comfortable painting area is useful to concentrate on the painting process.
One can use clean piece of plywood or thick cardboard and paper clips or tape to mount the paper on the board. It is advised to keep the desk tilted as it easier to work and control the flow of washes. You may frequently have to rotate or change the direction of the board to apply wash from top to bottom or side-to-side. That is why it is easier to use drawing board than desk.