I noticed when preparing some rounds of .338 win mag with 2 grain increments that each lot was a couple of hundredth of a mm (0.001") longer as the powder charge increased.
I suppose this is due to more powder under each bullet as it is seated, but I have never noticed or thought the charge could influence the seating depth.

Has anybody else experienced this?

Yep, and that's where a crimp comes into play.

Yes. It can/does change w/ some powders ---different amounts---over time.
For example. Imr 4831 w/ 180g slugs in the 30-06.m

ONE thousandth?! Please. Your seating depth will vary more than that normally.

Actually yes, I checked my reloading log and found that it varies by 3 to 4 (0.011-0.015") tenths of a millimetr, per 2 grain increase in charge.

Now, that is different; 4 TENTHS of a MM is .0157 inches, In your original post you were talking in terms of Hundredths of a MM (.001 inch), Big difference, tenths and hundredths.
Anyway, seating depth should be adjusted for your magazine, throat, pressure signs in your rifle, and best accuracy. Best to work up your own loads. Or just go with the book for most uses.

You're right, in my attempt to speak in a similar way to the imperial measure system I got it wrong.

2 grains gives 0.3 - 0.4mm OAL difference.
What I dont remeber is if that was tge total difference between the lightest and heaviest charge or between each individual charge.

I should check it when I get back.

In any case, your OAL is determined by you, your magazine, crimp groove, throat, rifle, and myriad other things.