If you want your product CE marked then you'll need to get it tested either way. The emissions from your product will depend on the other components in your design, the layout and the enclosure too, and it's certainly not the case that you can buy a CE marked power supply and then claim emissions compliance on that basis.
A CE marked power supply will save you some time and effort when it comes to getting safety approval, though - but that has nothing to do with the class A / B certification.
In my experience, many power supply manufacturers have trouble understanding that in order to be usable, they have to not only pass (particularly conducted) emissions on their own at full load; they have to pass with good margins under all operating conditions. Without margin to spare, once their PSU is connected to a real circuit which inevitably generates some noise of its own, the complete system cannot pass an emissions test. Whilst their product may technically be legal and compliant, it's not commercially usable.