Testing for Testing's Sake

Could a blood test gauge your risk of suicide?

Yes, maybe, but not this one.

This gene test might determine some kind of overall lifetime risk, but it won't be sensitive enough for immediate assessment.  
Psychologists are already perfectly capable of guessing wrong.

If they really want to check blood for acute suicidal tendencies, they should try testing for bacteremia.  Bacteria in the blood drastically reduces orexin levels while raising cortisol levels- which can cause depressive panic attacks.