? about testing blood for DNA info?

I was thinking about this the other day. I was wondering if a person recieved a blood tranfussion and then soon after committed a crime where blood evidence was left behind and successfully recovered, would it be possible that the blood donor could be identified instead of the person committing the crime? I know that this would be very unlikely but I am wondering if it would be a possibility. I understand that a blood transfussion does not involve total replacement of a person's blood. I am just wondering if it would be possible for tiny blood specimen that could be used to test for DNA be the donor's. Again I know this is very unlikely, just wondering if it could be hypothetically possible.