You could but it would be really stressful on the PSU. You can get the gpu and then get another psu when you have enough money. For the 7970 to work you will need a molex to 6pin adapter.
Also, i would remove those 2 HDD's and use only one while you are on this psu.
PSU spec:
+3.3V@20A, +5V@20A, +12V@34A, -12V@0.5A, +5VSB@2.5A
GPU needs about 17A max and cpu 7A max on 12v both. Thats within the 34A available on the 12v rail.