Yes. My city's blood bank does with the max being 17 point something.
Just make sure you are well hydrated when doing it - supposedly the number increase when you are dehydrated. If you are too high maybe take a few days off and consume more water and hit up another one.
I actually had to go to my doctor and get a referral. Next time I might just get the items needed and have my gf do it as she's done the phlebotomy course.
They are supposed to deny you if it's too high, but they almost always break the rules on this one and allow you to give anyway.
Why would they deny? Isn't it a "win win" for everyone?