I'd say it matters but don't know how to quantify how much. Even NA 220 & 240D's have them. If I had to run without one it would be only for a short time, driven easily and on synthetic oil.

As a reference point I've seen US gas engines without them while the same model in euro trim had them. Removed a cooler on a '81 380SEL because a euro radiator was $$$$ but the car would never be on the Autobahn. Didn't have any problems but it was a NA gasoline engine.

Good luck!!!

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"Rudeness is a weak man's imitation of strength" - Eric Hoffer