First, it is possile to get eel grass in your engine intake (either while motoring around a harbor or other area at slow speed; or just idleing waiting for a fuel dock, etc.)
Secondly, if you use your engine to charge your batteries, you'll have the same situation as a generator.

We've had the most issues with bot generator and a water cooled refrigeration system (AC or cold boxes) is the more likely problems because you're relatively stationary.

If you only have one or the otherm then I'd leave the filter basket inside the boat for a bunch of reasons. You want to be able to see what's causing the blockage; you can visually inspect the flow through the strainer; AND you can clear it while at anchorage or under way.