Healers usualy have (rather can have) a very big impact on the game.
Basically it's the healer who allows his team to go heavily offensive and stay offensive depending on how good he (the healer) is.
A bad healer will usualy have bad positioning and get easily cc'd, along with bad situation awareness, thus easily tunneled down, making his team stay defensive, lose momentum and waste cooldowns, which usualy means losing.
That said, any healer is viable for carrying, altho disc priests are kinda lacking atm.
Demo locks are easily the best to "carry" in mists for 2v2 , I have had a lot of teams focus my partner (hunter) and then I solo after. We have amazing self heals and shields and to top it off all our burst +meta is on short CDs play it right and ur an ur harder to beat then a blood dk