Don't think so.
That's because it takes time to process blood and blood products
and whether the blood that is donated becomes Packed Cells
Transfusion or Fresh Frozen Plasma or Platelets etc depends on the
stock of blood and blood products at the time. What's in greatest
demand will be replenished first.
Due to these, I think it may pose a problem.
Still, you can go there and make a request. But remember, even if
the blood you donated doesn't go to the person you wanted to donate
it to, it will still ultimately save lives. 
