Does painting (non-conductive) over the top of a grounded metal
enclosure affect its ability to absorb/block RF interference?
No, the idea of an EMI enclosure is to create a faraday shield around something to block electromagnetic waves around whatever it is enclosing. The shield itself needs to be conductive to be effective and have adequate skin depth, on the inside of the shield the electric field is zero (assuming there are no radiators on the inside). (The skin depth needs to be larger for a faraday shield to be effective, but for most metals anything more than 5mm is effective against anything above 0.1Hz). And watch out for anodization also, which is an oxide layer on aluminum and not very conductive.
For a faraday cage to be effective, it needs to be conductive and continuous as possible (slots and apertures can provide inlets for electric fields to bleed in). This also means that conductivity needs to be maintained at the seams of the enclosure by not painting junctions, using conductive gaskets and flanges that cover seams. (and any shield\conductor interfacing to the enclosure also needs good conductivity and no paint)
As long as the surface of the enclosure is conductive and continuous, it will have the same blocking power even with materials of different conductivity on the outside. If anything the paint will attenuate high frequencies or change the reflection (because any two materials that have a boundary have reflection and transmission coefficients).
In short, adding paint to the surface of a metal enclosure will not change the conductivity of the metal underneath (unless there is some kind of severe chemical reaction, which is unlikely). And at the end of the day it is the conductivity of the metal enclosure that matters most.