If you don't paint it how do you prevent barnacles and oysters from making it their home? A quick search of past forums on the subject on Google revealed an interesting comment "if antifouling paint attacks plastic a bigger problem is the hull is made from plastic." Other comments suggest not to use "ketone based paint" but that water base and other solvents are acceptable.
Here's directly from the Airmar website, the company that makes transducers
http://www.airmartechnology.com/uploads/InstallGuide/17-355-01.pdf "
Anti-fouling Paint
Surfaces exposed to salt water must be coated with anti-fouling
paint. Use water-based anti-fouling paint only. Never use ketonebased
paint, since ketones can attack many plastics possibly
damaging the multisensor.
It is easier to apply anti-fouling paint before installation, but allow
sufficient drying time. Reapply paint every 6 months or at the
beginning of each boating season. Paint the following surfaces
(Figure 2):
• Outside wall of the insert below the lower O-ring
• Paddlewheel cavity
• Paddlewheel
• Exposed end of the insert
• Exterior flange of the housing
• Bore of the housing up 30mm (1-1/4")
• Blanking plug below the lower O-ring including the exposed end