You really would be running a risk - bad PSU's can fry a whole system. It's a Corsair power supply, so if you trust the brand enough to run this risk, you can, but upgrade ASAP, because that PSU cannot even be trusted with a 1060, forget a 1070. I would highly recommend a better power supply before any upgrading.
In the worst case scenario? Yes, it will fry your GPU. Not just the GPU, but pretty much everything else. I had a PSU go bad on me, and I had to get my HDD, CPU cooler, memory, optical drive(didn't use it anyway haha) and motherboard replaced. Don't have a GPU, but that would have been fried as well, I'm sure.