I have looked at all the MOT Special Notices that appear on the Mot Instruction Manual that I could find and see no reference to the non paint/cover over of repairs to bodywork, though I may be missing something. It woulc be good if a screenshot of this Special Nqtice could be posted to clear this up.
As regards repairs, the MOT tester can ask the vehicle presenter to remove any coverup of a repair if he suspects the repair to be subatandard so a full inspection can be carried out, but this has always been the case.
Yes of course you can paint it. But if he thinks you're trying to hide something he can ask you to clean it off. I doubt this would happen though unless you were taking the piss like covering it in MOT paint and then driving through a farmyard.
However now that my car is exempt I have covered some (very sound) welding repairs with fibreglass in the wheel-arches in order to prevent further rust and create a sort of wheel-arch liner. If it still needed MOTs this would be risky because he might think the repair just consisted of fibreglass and nothing else.
The MOT inspector will pass the typical patch on the floor if he can see welding spatter all around the edges, even if the welds are shockingly bad. They aren't assumed to know anything about welding. In practice even a half-decent "continuous seam" weld on a car will not be water-tight, so it's worth sealing it up with something. But I guess you only have to do that on one side.
If the weld is somewhere visible on the body you will want to do a butt weld, grind it flat, skim it with a bit of filler, and paint it. The tester has no reasonable way of checking if that is a continuous seam weld anyway.