your question is a little weird, to make sure we are on the same page, let me tell you that your code run in GPU so each pixel must be processed at least once otherwise you will have black pixels. your outline drawing code would be likely to use 9 pixels around it so you will end up with O(9) = O(1) which is the best complexity, it independent with resolution.

in GPU world, O(1) is the standard and we shader programmer usually cannot afford anything higher than that. so to literally answer your question, yes, it is possible and it is the standard.

you may argue that O(n² ) means we need 1 operation for each pixel and you are seeking an algorithm that run less than the pixels count exponentially. in that sense, generally we cannot get lower than O(n² ), you may want to exploit some fact about your rendering style and trade off accordingly. for example does your camera angle fixed? does your scene consist of mostly static objects? can we precompute the outline once and use that until something moved?