Generally a sub-assembly isn't required to bear a CE mark in its own right, but since the finished product in which it'll be used will have to pass CE certification testing, a sub-assembly that prevents the finished product from passing will be rejected by the customer on commercial grounds.
It's an argument I've had with power supply manufacturers on several occasions. A PSU gets its CE mark and does indeed pass conducted emissions testing when powering a dummy load resistor. However, it fails when powering something that doesn't draw full power, or which produces even a fairly modest amount of noise of its own.
I try to get the point across that a PSU can't just scrape under the limit line under one set of conditions - it has to pass with margin under all conditions, or it's unusable. The first thing I do with any potential new mains supply, after checking that it's basically functional, is take it down the EMC lab and have a sniff. If it's too noisy then it goes in the bin - no excuses.