Vant is spot-on. Depending on how picky the retesting company is, they can refuse to even test the bottle if it's been painted. Many will even require that any stickers be removed prior to testing as well.
Part of the Hydrotest procedure is a visual inspection- for a steel tank, they look for dents, signs the tank's been subjected to heat, or mechanical damage like gouges or stress cracks.
On a fiber-wrap (or fibre-wrap for you Brit mooks) they look to see if any of the fibers have been cut, damaged or broken, the epoxy/glass matrix has been stressed or damaged, and so on.
It is not unknown for people to have a small tear in the fiber and to "fix" it with a bit of 2-part epoxy, or superglue, or fiberglass resin. Said patch is then "hidden" by the paintjob or a sticker.
Given that the fiber shell is a major portion of the bottle's strength- better than 80%, as I recall- even minor damage here, if not caught in time, can lead to a catastrophic failure.
I don't know how the UK testing is done or checked at the events, but the pickier US events can refuse to fill a painted or excessively-stickered tank. (Realistically though, fills are done either by the player or by some peon who barely knows which valve to yank, so checking isn't as thorough as it could be.)
But I'd bet money the actual hydrotester will refuse to test it if it has an opaque paintjob on it.
Doc.