It depends on what it's being done for. If they are looking for reasons for infertility, they might not test for infection. They will be probably looking for motility (the movement of sperm), the number of sperm, and the shape of sperm.
https://www.healthline.com/health/semen-analysis
If they find any issues with any of these, they might do further testing, like for infection, but it's not a normal first step. STD testing, by urine, might be a step that's done at some point, but semen testing for STDs isn't as accurate as urine testing.
