I doubt it draws 400W. I run an i7 3770K and a 7950. Calculated load is around 325, and your 1070 uses less than that. Unless you've OC'd your CPU and GPU it should be much closer to 300W.
Are you going to buy that PSU or do you already have it? If you are going to buy it I'd look for a better model. If you have it already you are probably ok, but I wouldn't OC anything or run a demanding CPU.
500 watts will be enough as long as the PSU is high quality. The only 80+ White EVGA 500w I know about is close to crap quality. I recommend a higher quality PSU if you haven't already bought, or if you already have it i suggest upgrading if you can afford.
It depends on what the rest of the system is. I have an I5 4670 with an MSI GTX 1070 and the entire system draws 400w max. If you are buying a new PSU, I would opt for a larger one to be safe for a few years.
I doubt it draws 400W. I run an i7 3770K and a 7950. Calculated load is around 325, and your 1070 uses less than that. Unless you've OC'd your CPU and GPU it should be much closer to 300W.