i can only speak of my own experience in this. i have done both seperately and together. oil pulling is unique. it shortcuts the normal channels of elimination and removes toxins that dont have to otherwise be dealt with. someone likened it to a third kidney. i have compared it to a disposable mini liver. it could be both, but i would certainly swear to the latter.
those who do not otherwise ingest a good amount of plant fats in their diet are sure to get double benefit from the pulling just as you said - by absorbing some of the fats into their body. doing both is the way to go, no doubt about it. and put it on the skin too.