For a little while, sure, depending on your other components of course. But it's sure to let the smoke out that the engineers so diligently worked to put into it after extended periods of maximum draw, especially as it could easily peak beyond 650watts.
I have a 14 core/28 thread Xeon, the whole system uses about 150watts under load, and then I have a AMD FX something or another (8350?) that uses a whopping 240 watts under load, for a measly 4 cores/8 threads. I've measured my Radeon R9-280X's (basically same GPU as yours) as using an additional 225watts under load, but it's highly variable, up and down. (The measurements are from the wall, not the power supply.)
Long story short, I wouldn't recommend it long term. A week or two, eh, sure, the PSU should shutdown rather than let the smoke out, until you get something closer to 850watts.