I would do the project in two steps. The mud would be so thick that the paint would be too diluted to make a proper textured statement.
Consider mixing mud with water until you get a pancake mixture thickness, then roll on this on preped walls for your texture, then wait a day, and then do the painting.
There is an additive that you put in paint that will make a wall texture like popcorn but much smaller popcorns. Its almost like big grains of sand. You have to keep this well stirred as the grains settle to the bottom of the paint can. I do not like this as it puts up erradic texture.