I was wondering... If Ebola attacks immune cells and causes immunosupression, then shouldn't we see death in Ebola patients due to secondary infection?
Yes, we should. But Ebola doesn't completely immunosuppress us, or there would be no survivors.
Ebola kills by overwhelming the body before enough antibodies are formed to fight it.
If you're one of the survivors (as about 40-50% are, more with good care), you'll have antibodies to Ebola in your blood which might help someone else infected with Ebola.
If you're not one of the survivors, it's still likely you'll have some antibodies, but the shock your body goes into from all the dead cell products in your blood (which - overly simplified - causes a cytokine storm -> leaky capillaries -> fluid balance problems -> end organ failure -> death).