Oh lol, the Evga P2/P3 is among the best psus on the market.
And no, your ups doesn't have to follow the psu. With a gtx1060, you are looking at a gaming load of maybe 250w. Having a 650w ups just means you have time to spare, and no matter how hard you are gaming, the ups can take the brunt of any power outages with no loss. If you had a 600w load you'd be limited to what the ups stats say is time at full load, usually a couple of minutes.
One other thing to consider in your search and thats your ups. With Active PFC units such as that Evga P2,/P3, they can be extremely picky about sinewave output. With APFC it's pretty much a must to have the ups output ad Pure Sinewave. This gives a consistent flow of electric along the whole curve. The issue with simulated sinewave or square wave is that while it may somewhat resemble a sinewave, it isn't. Yes you get the ups and downs as needed, but during the transition from up to down and vice versa, there's actually 0v. Any decent DC-DC psu has APFC and will see that 0v state as being a power outage, and shut off.
For instance, I have 2 pc's. One has an older group regulated Seasonic M12-II 520w, the other a Evga G2 550w. I have 1 Minuteman Pro 700, which has simulated sinewave. The ups works great on the Seasonic psu, but will not work with the Evga G2. If I pull the wall plug, the battery kicks in and Seasonic stays running, no issues. The Evga shuts down instantly.
This isn't a design flaw in the Evga, it affects any psu with active PFC. Basically simulated/square wave ups with an APFC DC-DC psu is no better than a really good surge protector.
As good as the Evga is, and it's very good, with your system, if you have a simulated sinewave upc, you'd be better off with the Seasonic M12-II or its Antec version, where it'll work with a non-smart ups. If your ups is 'smart' or pure sinewave with AVR, then by all means jump on that Evga Platinum.