Can a root canal affect recovery from sports injuries?

Positively. It is not a good idea to have any type of infection in your body. A root canal treatment is normally done when you have an infected tooth. If you are getting over a sport injury than you want your body or immune system working trying to heal your injuries and not fighting an infection.
Sports and rct. Not likely unless there was dental damage during the injury.
RCT\Sports injury ? I see no correlation and wonder what prompted the question. Perhaps you can repost your question with more information.
Root canal. I don't see why it would affect recover of a sports injury in another part of your body unless the dental infection had become systemic.
Root Canal & Sports. If you are referring to root canals and effect on teeth while playing sports, then it's important to first get your tooth crowned, then wear appropriate protective gear for your sports to protect your teeth. I'm not familiar with a root canal actually slowing down recovery from sports injuries such as broken leg or arm but infections does need to be treated for overall health improvement.