Yes and no. Yess, it is possible to fracture or rupture a testicle. This is treated surgically. As the other testicle will produce testosterone, sexal functioning should not be affected by the loss of one testicle.
Testis trauma. Yes, a testicle can rupture. The scrotum on the affected side is very swollen and tender when this happens and surgery may be required for repair. If ignored, the individual will likely have a long recovery but ultimately this should effect sexual function if there is a normal other testicle. Loss of a testicle may impair future fertility.