Could a faulty heater matrix cause overheating on a nissan micra?

I have an r reg nissan micra which has recently been overheating. I have changed the thermostat and the cooling switch, however the problem has not went away. Add to this the fan will not work on the radiator unless powered directly from the car battery, and even when set up and working like this the engine is still overheating. I have decided to tgake it to a local garage who have quoted me �200 to fix as they are saying that the heater matrix is blocked and this is causing the overheating, they have also said that the fan must have been working constantly with the engine overheating and as a result this has burnt out part of the ecu or something. Does this sound like it could be right and if so is it a decent price for the work.