Yes... You Should or MUST get bad Frames per second or Slow/horrible gameplay.... But it has noting to do with your R7 250... You Need a decent CPU to play recent games.
So, either Replace your processor with A8 6 or You can choose the RISKY Way tog get Better performance. I am talking about Overclocking your Processor... Still you will have tough time to get Stability because it is a Non 'K' processor...
Get a decent Cooler and Overclock your Crappy processor... If you can atleast 4 GHZ then you CAN PLAY Recent GAMES at LOW-MED 720P without any lag/shutter....
Best of Luck...
[ if you no idea about overclocking you can get tutorials from youtube, or you can ask this forum, but we will need your Whole CPU Specification]