Yes, you can climb out of silver by playing support. So, I'm not participating in the poll because there is no correct answer to it: all roles have an impact on the game; it is a team game, making all roles necessary as parts of the team.
Your builds look good, as well as the amount of wards you're putting down.
Your runes could use some work, in my opinion. You have two hybrid-style pages, one AD page, and one tank page. You should get rid of one of the hybrid pages, and for the other hybrid page use all 9 hybrid pen marks. On your tank rune page, get rid of the AP quints for some sort of tank glyphs. In my own tank page I have health per level yellows and flat armour quints, which is just my preference, but the flat AP quints are not as useful on a tank as tank quints are.
Other than that, I suggest looking at your gameplay and watching gameplay videos and guides. Your positioning may be off or you may be warding ineffectively, but I can't see that from match history alone.
Hope this helps a bit. GLHF!
