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It depends on the source material.
As luck would have it, I just recently got the 4K Blu-ray of Lawrence of Arabia, and it is very very grainy. Much more so than the 4K version of Rear Window, though that has a lot of noticeable grain.
Fortunately, some theaters still occasionally show classics like these, so when Lawrence comes around, we should find out. Hopefully. Assuming it comes in on big reels of film, and not over a digital link.