I hate to say it, but it really wouldn't. The R7 250x simply can't keep up to the graphics card in the PS4 or even the Xbox one, which are more akin to a 260x or a 750ti.
Personally, I'd go with something more like this build:
https://pcpartpicker.com/user/Cloudyy/saved/#view=R7Ckcf
Instead of the Pentium, I chose instead an Athlon 860k. The Pentium is a great processor, but more and more games are having issues with dual cores and the Athlon will most likely prove to be a better investment at this price point.
The other big change I made is the 270, this graphics card will run circles around the 250x and it's only about 140 bucks. ( http://anandtech.com/bench/product/1126?vs=1080 )
Still, the build manages to be only $411 dollars before mail-in rebates.
This is of course taking some advantage of current sales, but similar deals for similar products can be found at pretty much any given time if you look on pcpartpicker.