guavasauce
Distinguished
from the spec sheet, the 6970 requires roughly 19amps from the 6 and 8 pin cables. your power supply has 2 12v rails, each with 38 amps, so yes, you will be just just fine (full system with fans and drives).
your home server will also be just fine on either of the 4xx watt psu's.
your home server will also be just fine on either of the 4xx watt psu's.