Could damage to your genitals affect your offspring ?
If the damage is to the genitals as a bodily organ, it might cause you to have fewer or no offspring. Chemical or radiation damage to the actual eggs or sperm could cause the same thing, plus possible birth defects to the child.
Depends what the damage is
Depends on what damage was caused, and how severe. Some males can damage the testes and have "blanks", but you can also fully recover from damage there. Just depends