Will It Bottleneck My Athlon CPU?

[Pandro]

Ever since I started the learning curve of computer building, this site really helped me learned the basics of computers and learned the terminology and stuff like that. This is my first post so go easy I guess. But I am asking, does my AMD Athlon ii x4 635 bottleneck the R7 350?

The R7 350:
https://www.newegg.com/Product/Product.aspx?Item=N82E16814202237

Here are my full PC specs:

AMD Athlon ii x4 635
4GB DDR3-1333mhz
OEM mobo from HP
HD 4200 IGPU
750GB of storage
Windows 10 activated
250 watt power supply (planning to upgrade the power supply to a 430w or 400w from EVGA)

My budget is around 50-60 dollars if you are going to recommend another GPU.
New parts are preferred. Although I could go with used PC parts, but I had a bad experience buying a product from Ebay.

 

[CountMike]

No it shouldn't but whole system may be a bottleneck.