Current should travel without issue through a layer of paint that thin. Any resistive or non-conductive material (paint, paper, air, etc) has a given level of resistance, after which point current will travel across or through it.
Air is a resistor, but the charges built up in the atmosphere during a thunderstorm can become high enough to overcome the resistance of the air gap and the result is lightning. A shock on a door knob on a cold dry say when you're walking on a synthetic fiber carpet is the same thing, the smaller air gap just before you touch the door is overcome by the charges built up in your bode.
The paint covering machines like this will only be slightly resistive, if at all. They may even be impregnated with metal particles so that they are conductive, rather than resistive. It will only take a very small differential between the energy in the clip (your body) and the chassis to bridge the gap of the paint and establish a ground connection. The direct connection between your body and the group strap and between the clip and the chassis will prevent any sparking when any transference takes place.
However, all that being said, the ground strap will only work connected to the computer when the computer is plugged in, and you don't want to work on a computer that is plugged in. The better thing is to connect the ground strap to a completely different item that is grounded (plugged in with a grounded plug).
1Thanks for the reply. In the picture, the power supply is bottom left, and is completely covered in black paint too. Or have I misunderstood? – Clare Macrae – 2011-12-21T19:32:37.190
Is there any static electricity on the British Isles? ;-) I always remove a mobo from a case when installing RAM and use Anti-Static Polyethylene Foam. – Aki – 2011-12-21T19:50:45.347
@ClareMacrae: you're right, it's a power supply. It is hard to see if it is painted completely. I'll amend my answer. – haimg – 2011-12-21T20:01:31.540
To anyone else puzzled by @Aki's answer, wikipedia tells me that a 'mobo' is a casually shortened motherboard :-)
– Clare Macrae – 2011-12-21T20:33:23.660Chances are you can probably conduct even through the painted components. Probably anecdotal, but in reality I do hundreds of RAM swaps a year and I rarely if ever use an anti-ESD strap. Do the replacement on a hard surface (i.e. NOT carpet), discharge any ESD from your body on something grounded (PC case, metal surface, buddy, etc.), and then seat the memory. – Garrett – 2011-12-21T20:53:36.943