Is mental health related to male fertility?

Yes. Stress is a factor in sperm production and delivery. Stress centers in the brain reduce FSH and lh, the hormones that trigger sperm production. Stress reduces erection and ejaculation, a problem for sperm delivery. Stress reduction can improve these problems.
Yes. As I have always said, "a good reproductive body is an overall healthy body." stress can influence fertility. Diet, weight can also. See the google lecture i gave: http://www.Youtube.Com/watch?V=s1dxl-wvjzk;list=pl1f9ba7bfff4925f9.