Maybe this has nothing to do with the oil pressure at all, and is associated with the glow plugs being on for a few seconds of operation after the engine starts. Once they go out the usual Diesel combustion process takes over and you get the noisier and clankier Diesel typical clattering and clanking?

Sounds odd, but not like an oil pressure cause and effect to me. Good oil films and chain tension make things quieter, not noisier. So, as you get the benefits of oil pressure coming on, something else is going away, and it dwarfs the oil pressure benefit. The only thing I can think of is that the combustion process, minus the benefit of a glowing hot plug tip to get it going quickly, changes and you are left with something noisier until the engine completely warms up. Just a theory. Jim

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Own:
1986 Euro 190E 2.3-16 (291,000 miles),
1998 E300D TurboDiesel, 231,000 miles -purchased with 45,000,
1988 300E 5-speed 252,000 miles,
1983 240D 4-speed, purchased w/136,000, now with 222,000 miles.
2009 ML320CDI Bluetec, 89,000 miles

Owned:
1971 220D (250,000 miles plus, sold to father-in-law),
1975 240D (245,000 miles - died of body rot),
1991 350SD (176,560 miles, weakest Benz I have owned),
1999 C230 Sport (45,400 miles),
1982 240D (321,000 miles, put to sleep)