Will a first void urine leukocyte esterase test most likely be positive in men who have some sort of sti that causes urethritis?

Doesn't matter: See my reply to identical question that referred to Mycoplasma genitalium. Same answer. If no symptoms, and negative tests for gonorrhea and chlamydia, asymptomatic urethritis is not a health problem and doesn't need testing. You're obviously obsssed witih this (maybe your 4th or 5th question?) -- probably no need. Work w/ your sexual health clinic, but HealthTap cannot help any further.