Ok, given that you said it currently came with an R7 370.... Looking at just a few reviews of various ones, Here on Tom's one review pegged an R7 370 at 12W idle, 107W Gaming, and 147W stress testing.
http://www.tomshardware.com/reviews/amd-radeon-r9-390x-r9-380-r7-370,4178-4.html In a different review on a different site, they pegged an R7 370 using 189w. http://www.digitaltrends.com/video-card-reviews/amd-radeon-r7-370-review/ Per Nvidia's own site, the GTX 970 requires 145w.
http://www.geforce.com/hardware/desktop-gpus/geforce-gtx-970/specifications
And last but not least, the GTX 970 on 450w psu has already played out in the forums 2 years ago.
http://www.tomshardware.com/answers/id-2315271/power-gtx-970.html
I stand by my original statement in that, yes it will probably work, and that it is a borderline situation. To further explain this, you may have additional components fans, hard drives, fancy led lights, and other things that add to the stress on the power supply. As others have stated though, and while i do believe your situation might work, they are right as well in saying that it isn't a really good idea to try this. It would be pushing the limits of what most people would consider a safe component situation, and you really don't want to damage things you've spent money on. Changing a power is an easy, and quite affordable thing to do compared to changing other components, and having a bit of piece of mind is nice