Whenever you place a blood drawn from a PC on the altar, you receive a message saying "You have already tested this blood before. While you are free to test as much as you like, you know that the House will not bother to reward further tests." - even when this is the first time you have donated that character's blood.
The only item I have found that rewards any house points is dragon blood.
I can confirm it's working. Blood tested while it was broken still counts as having been donated, but donating blood from a pc you haven't donated before now works.