Maybe not at the highest settings but on "high" you should be able to game on 3 monitors but dont take my word for it! the closest experience would be a year ago, I have a gtx 760 4gb (slower gpu) able to run 3 monitors on pretty high settings! SO I can imagine the 290(much more powerful than the 760) you having a pretty good time with 3 monitors! And in terms of the fx 8320, yes it is fine for 3 monitors, I used the fx8320 when I had 3 monitors originally at stock clock of 3.5ghz and at 4ghz and they both are completely fine!
honestly after reading this thread I feel like getting 3 monitors again!!!!
Hope this helps and the best of luck with your build!