Rim insulation in a tight spot

I would be hesitant putting any insulation in there with that plumbing in that space.

Unless that is a hose bib that you can drain prior to winter, putting insulation in that cavity will make that piece of plumbing much, much colder. You could get freezing where you didn't previously have it (depending on the area and nature of that supply piping).

The insulation (should you spray foam it or stuff batting in there) will dramatically reduce the warm room side air that can reach the pipe and they exterior wall.

By doing so, the cavity and pipe will become much colder.

If you have enough room and can get your hands in there (doesn't appear as such) you could stuff some insulation behind the pipe and in between the rim. Leave the pipe exposed to the interior air in this case.

Otherwise, my recommendation, leave it be.