No, if the house is using 3kw and the system is producing 3kw it would use the pv, if the house is using 4kw and the pv is producing 3kw it would use 3kwpv and 1kw mains, if the house is using 1kw and the pv is producing 3kw the it would use 1kw pv and export 2kw pv back into the grid.
Hope that makes.
Ok, I was (mistakenly?) going by what the client told me. I've learnt alot of useful stuff this evening. At least now I can go back with the EICR completed with issues observed & recommendations on how to bring it all up to spec