I've got the standard 32 computer still... so I'm ok there.
I thought the whole idea of an engineers report was that they could verify that mods are mechanically sound. Then the emission test will show that emissions are ok... if both are fine then everything is ok.
As long as your car is tuned properly and you don't have cams, etc and you have a good cat, you wouldn't have anything to worry about with an emission test, surely??