I wouldn't use the soft scrub unless you can't get it clean with just a wet rag or sponge. Cleaners will tend to leave a residue behind that will then be in your water and can contribute to foaming. I have found that putting distilled white vinegar in a spray bottle and diluting it 50% with water makes a great solution that leaves behind no residue. If you do use something like softscrub, I would wipe it with a damp towel afterward to remove the residue. You can certainly hose it down with water while keeping the drain open, but most of it will not rinse out.
It doesn't matter if you remove the filters or not when draining, though this is a perfect time to clean them as well.