The areas under my washboards would get dirty, especially during winter lay-up.
Some of that dirt was mold from the dampness and lack of sunlight due to the boat being shrink-wrapped.
If you are sold on painting, proper prep will be needed which should start with a good cleaning.
Get yourself a spray bottle like those sold by Home Depot or Lowes and fill it with 50% bleach and water.
Wet the underside with a hose and scrub the area with a good boat soap and Simple Green.
If there is any wax under there, the Simple Green will remove it.
Rinse the area again, they spray with the bleach solution and walk away.
Come back later after the area drys and lightly rinse again with a hose.
You might find that you don't need to paint.