Carrying as support?
The support role is very unpopular in League of Legends when you think about how many players prefer the other roles, the queue times for support are the shortest, meaning fewer people are playing it.
This isn't some intrinsically connected to League of Legends, support or utility roles are often less played, but that doesn't mean they don't have any impact in the game, even in League of Legends, support is a very important role that can change the outcome of the game in a lot of ways.
The importance of supports is often sub estimated on the community depending on what rank you play on, and then most people won't even give the role a try, while in fact, the ranks where support is most sub estimated are the ones where it is easier to have a big impact in the game.
A support character, depending on the champion you pick, cannot carry a game with their own hands, you will depend on the ADC to be able to play the game at least in a decent way to give the game a positive impact early on or things will start to fall pretty quickly. Some champions will make you able to carry even with a bad ADC on the support role, they are the few damage support characters.
Zyra is an example of Damage Support who can get an overwhelming win-rate, it is a champion that will not be completely unplayable if your ADC is not playing that well(or is trolling), another champion like this is Brand, he is an excellent Damage Support who can bring justice to a bad ADC, he doesn't need a lot of items and he can get those just with his support item.
Why play a Damage Support?
Most people will play those because they like it, or they don't want the game to be a gamble on a good ADC in low ranks, it is a good way to go if you enjoy the role but feels frustrated in some games.
The Damage Support still provides the vision to the team and plays as a support, so some builds won't fit as you don't get a lot of gold compared to the ADC.
Besides Zyra and Brand, other champions go well there, like Lux, Veigar, and Pyke, they provide not only damage but utility and still can do support things without completely ruining the build.
It is not a mandatory thing for winning games to play as a Damage Support, your usual support can still get good win rates if you don't mind some very awful games sometimes, it is something that always happens sometime or another, but you can do get games where you have an ADC who can do their job and your skill as a support will be the factor influencing the lane.
Can a Support carry a League of Legends game?
Supports can provide a significant amount of opportunities for the game to be won, not all other 4 players will be bad at the game, and you still can help your team members to excel with whatever you have going on in your kit.
In theory, utility simply cannot compensate a game if other players don't take the advantages you provide, but that's rarest the case, often there is something that the support champion could have done better to achieve a better result but it can be overlooked by the players themselves.
In practice, carrying as support is possible with game knowledge, League of Legends isn't a perfectly balanced game like tic tac toe, the support is a big change in the early game lane balance, where two ADCs are often with around similar damage output, and the supports make the required weight to one side or another to win the matchup.
Having game knowledge can further make the Support champion able to impact more than one lane, as it should be, and this can affect the outcome of the whole game drastically.
However, the impact made by the Support player isn't often statistically shown or something explicit in the game, this makes the role often looked down upon or misunderstood, the kills and deaths are where most eyes are at but the game isn't just that.
So although supports have great potential, they are overlooked a lot in low ranks and it sparks doubts about if they are good or useful champions at all, but don't make that fool you, they are silently changing a game for better or worse in a big way!