Oooh ... an engineering question...
I will try to answer it - but since I live in South Africa and therefore have no need for radiators, I might not fully understand the way in which these things are controlled. I assume that there is a thermostat in the system that turns the hot water flow on and off in response to the temperature of the room (if I'm wrong about this, then parts of this mail might be rubbish).
Chris - you would be right if the radiator was an electric heater - which produces the same amount of heat regardless of the conditions around it.
However, in a water-based system, the rate of heat transfer is (among other things) determined by the difference in temperature between the hot water inside the radiator and the air outside it. The greater the difference in temperature, the faster heat is transferred.
If you "box in" a radiator, you create an insulated air space around the unit that heats up. As a result, the difference in temperature between the water and the air up against the radiator will decrease and the rate of heat transfer will drop.
It's the same as when you put on a jacket - the temperature of the air against your skin increases and the rate at which you lose heat drops - making you warmer.
However, there is a BUT ....
This limitation will only exist if the hot water is flowing to the radiator constantly (in other words - if the radiator itself is the limiting part of the system because it is too small for the room).
If the radiator is big enough - and the hot water flow to the unit doesn't happen continuously, then the system might be able to cope with being covered. It will just open the water valve more often in order to get the required heat to flow into the room.
So there is no "hard and fast" answer to the question. If you have a really big radiator, then it might cope with being covered - the water will just flow through it more often.
However, if your radiator is on the smaller side (which is probably more likely - because people don't normally install thing that are over-sized) then covering it might limit the amount of heating it can do. Even with the water flowing through it continuously, it might not be able to get enough heat into the room.
I am sure I have now confused everybody...
Cheers
Steve