Many people paint their tanks and I can't find any law that says you can't. I don't see any reason why plasti-dip would be any different. I would make a call to your favorite filling station first though and ask what they say. The person filling the tank is supposed to watch for condition of the tank to make sure it is safe. There may be an argument that because it was painted with plasti-dip that you can not see any underlying rust, cracks, or other damage. I personally can't imagine I would run into this issue but it may be a concern for some who may end up getting a fill from an overzealous station. Your filling station may also have a company policy that says they won't fill a painted tank for whatever reason. It's best to call before wasting the time and supplies on something that may need to be taken off.
One thing to watch out for is color. Propane tanks are most often white because of the heat reflecting qualities. Painting the tank a darker color will attract more sun and gain/retain more heat. A higher temperature equates to a higher internal pressure. This could lead to blowing the over pressure safety valve, especially on a tank left in direct hot sun.