I believe the risk of injury, disability, and/or death does influence young and talented athletes when they consider offers to compete professionally. By the time a student receives such as offer they have a lot of experience in their sport of choice. They have seen examples of injury and disability, due to the sport, by that time and I'm sure it impacts their lives.
Many young talented athletes are at great risk for injury or disability in professional sports. This is why I believe that they contemplate the possibility of injury or disability before decided to play professionally in their given sport. They sometimes may even contemplate the possibility of a young death. But I do think they consider it.
People exercise, people try, and people believe that by working hard they can achieve their goals, but people can get heart. As a matter of fact accident happens and we can't predict to prevent them. Sprinters can get heart while they are running so fast they may sprain their ankle, they may hurt their hamstring, and they may fall, but that doesn't mean that they should stay away of exercising. Also, soccer players may get hurt while they are playing together. But the accidents are always there; by exercising the right way about what we are doing and appropriate tools of training we can avoid injuries.
I believe the goal of about every talented, young athlete is to be recruited to play professionally. I'm sure they realize careers can be ended suddenly and unexpectedly by injuries, but I do not think that possibility deters many of them once they find out how much they will be paid. I believe they feel that a few good years would allow them to save enough money in case they sustained a career ending injury.
For the majority of athletes, competing professionally is the pinnacle achievement that they strive for. Apart from the obvious reward, money, a talented athlete can only test their levels of talent against other talented athletes. Competing professionally gives them the opportunity to prove themselves against the worlds best. The risk of injury is negated by that opportunity to compete.