The minimum specs for the 970 is a 500W PSU, so technically yes.
You run the risk with low-end PSU's. With the idea in mind of connecting a 970, people either get extra (600W+), or get a high grade (Gold certified) smaller one (550W)
From what I'm seeing, Allied PSU's are no good. I wouldn't risk it. You could fry your entire PC. Invest in a 600W PSU. You can get them for pretty cheap.