I wouldn't consider leadership as the most important characteristic for a project manager to have, but it's definitely important (in my opinion, organizational skills is the most important).
Now why is it important? Imagine a project manager with no leadership skills (well, for many it's not that hard to imagine, if you get the joke), how can he lead the herd (and it's a herd of cats!)? How can team members respect him, listen to him, do what he asks them to do? How can the team members give him the quality he seeks?
Employees like to follow an example, and what is the example that a project manager will set if he's not a leader.
Project managers who are leaders will motivate team members, they will challenge them and they will always get the best out of them. Additionally, they will not have to micromanage the project because the team members usually care about the project when they are managed by leaders: team members will ensure that when they say that a deliverable is finished, it's really finished, they will also ensure they meet the quality guidelines set by the project manager, just to satisfy him. Generally team members are much more productive under a leader.
The project will run much more more smoothly and efficiently because team members are highly motivated by the "leader".
A project manager with no leadership skills cannot motivate employees, and not only that, he can't even get them to do their tasks properly. PMs who are not leaders have to micromanage the team to ensure tasks are done, which will add insult to injury, and will reduce the team's productivity even more. So, to answer your last question, yes, projects may fail if they are managed by non-leaders, simply because tasks will never be done on time, and they will never be done according to the scope.