If you have a lot of spray coming in the boat more than can be coped with by the bilge pump then leave them down when running. Many drivers do this as a matter of course. What happens when you stop is a different matter though. Depending on the design of transom, trunk installation and where in relationship to the water line the through transom holes are, is whether the boat floods at rest with them down or not. If the boat floods at rest with them down then I personally would leave them up until you need them. You might forget they're down and come back to a burnt out pump and a knackered battery.
Another issue is that some trunks can foul the prop when in a tight turn, they are that close! So, these could only be operated in a straight line. To bail the boat, you would only want to travel straight anyway! So, if they might foul the prop in normal operation whilst down, then again, leave them up until required.
Hope this helps.