That's what I am saying - the filter is not part of the MOT so in answer to the OP, the answer is yes it will pass an MOT as long as the emissions are fine at the time of the test.
The MOT is minimum std and doesn't cover every part of the car, only the sections mentioned in the manual. Just because a vehicle passes an MOT does not make it roadworthy; it just means that the parts inspected on an MOT are correct at the time of test.
Another example of this type of area is after market HIDS. By law they should be self levelling lamps and have cleaning on them. BUT if aftermarket fitted many of them don't and so long as the aim and colour etc are correct, then it will pass the MOT. It doesn't mean they are legal though.
Same with tinted windows - not an MOT item and therefore will pass even if heavily tinted on the screen and fronts BUT will receive attention from the Polis and VOSA with their Tintmasters.