i am at the moment doing this experiment.
it took me 207 games to rise from silver II(after 6wins/4loss placements) to diamond 5. It was hell of a journey, i was also almost in Diamond 3 but got completely rekd and had a disgusting losing streak and ended up in diamond 5 again. I played only supports and most of the times i felt not having a lot of influence, in fact i felt like.. i was just supporting.
I think it is a fact that playing a champion that is the lowest level, has lowest amount of gold and in general spends most of his early game money for building sightstone and finishing support item, you will be the least influential. this also greatly shows up in the queue times as nobody wants to support.
so i'm testing this and smurfing as mid/top lissandra only(because i love her lol) but also to see how well i could climb with a generic champion that fits in many teams and is NOT deprived of gold/experience.
So far I only finished placements and ended up in Gold III with 8wins/2 losses.
Generally I want to see if I ever reach diamond with a mid/top champion because this whole role is very new to me for someone who only played support. and if i do reach diamond, will it take me longer than 207 games? will see :)
But to answer your question - it is possible to rise as a support. but it was hell of a frustrating journey. i just dont know if it is more frustrating than if you were a jungler or anything else.