Do you take Medicaid?
Do you have a sliding fee scale for people without insurance?
Those are two things that are required. The other question is whether or not the HPSA score would be high enough to even give you a chance at loan repayment. So even if you did get qualified at your site, but your score was below 14 or 15, there wouldn't be much of a chance of getting any loan repayment. If it was even lower, it'd be pretty definite you wouldn't get selected.
So, to check, I'd get on the NHSC website and search for FQHCs in the area to see what the HPSA score in the area is, to see if it is even worth it. I think there is a mental health HPSA score, so make sure you are looking at that.
If your score is low, but you are working for a non profit, your best bet may be the 10 year public service loan forgiveness if your income makes that an option. States also may have their own loan repayment system you can look into.