ASME Y14.5M-1994 2.4.1 addresses this "Where a part is to be plated or coated, the drawing or referenced document shall specify whether the dimensions are before or after plating."

So to American standards the drawing has to explicitly state whether the dimension applies before or after painting.  If the drawing doesn't say then it's ambiguous and arguably parts can't be rejected either way.

I'm not sure with ISO does though.

I'm thinking in machines and machines are assembled first and then painted. So I guess all dimensions in manufacturing drawings are without paint thickness (= paint thickness is added to drawing dimensions). I'm from Europe and I have never seen a manufacturing drawing with information about paint thickness. I saw drawing for parts which are coated after machining but that's something different.

If paint thickness was a critical value I would always add the information on the drawing. I learned that it is better to give information when important, regardless what the standard says. Who's benefit is it, if parts do not fit but the drawing complies to the standard?

You can not have a painted surface and a tolerance of +/-0.002. That tolerance 20 +/- 0.002 has to be on an unpainted surface. Period.
Next question: " Why would anybody specify +/- 0.002 on a painted surface"? Smells like the drawing was made by someone not having the slightest idea of 0.002 mm.

Sorry the 20 +/- .002 was purely an example.  The actual case is a much larger frame, with a very thick paint process, that can cause the parts to run oot.  The problems it's causing now mean lots of rework and re-engineering a number of parts.

Back in the UK we usually specified if dimension applied before or after any finish/treatment.  However, I couldn't tell you what if any spec it was in.