Can one suffering from pancytopenia get a blood-transfusion?

Yes. Pancytopenia means a deficiency in all three major types of blood cells - white, red, and platelets. A blood transfusion would help 1 or more of those. However, it depends on the cause of the pancytopenia. Some conditions could result in destruction of the new blood products fairly quickly.
Yes. Pancytopenia means low counts of red and white blood cells as well as platelets. When your red blood cells are low it is called anemia. Our red blood cells (rbc) transport oxygen throughout our body for our organs to use. Without this oxygen our organs will be damaged or ischemic. The best practice is to transfuse only as much rbc as necessary to prevent ischemia or end organ damage.