Maybe, but probably not. Most games don't make heavy use of more than 1-2 cores, even though many will lightly utilize more, and the FX-83xx's cores are not any faster than your FX-6300's. The FX-9xxx CPUs are terrible, often unstable at stock, produce insane amounts of heat, and cost considerably more than better-performing Intel CPUs.
Basically, you're at the end of the line with AM3+. You can get a bit more from your system by overclocking it, but AMD hasn't released a new core design since 2012 for that socket, and will be discontinuing it entirely (most likely) very soon with the release of AM4.