Play them yes, but there is no point in getting a new card as you won't see any difference due to CPU bottle necking badly.
EG a GTX950 can run BF1 at stable 60fps, 1080p medium - but even the fastest FM2+ processor hasn't a hope of getting close to that. (framerate drops into 20's on 860K)
I only chose BF1 as an example but it would be also be true of most games - a graphics upgrade would be a waste as you wouldn't see any difference unless you were playing at insane levels on a large resolution monitor (1440p or 4k) @ locked 30fps.
The issue isn't IF your CPU can play new games - it can to varying degrees, from decent, to acceptable to unplayable - but a graphics upgrade would be wasting money.
A 2nd hand H81M and Haswell i3 or i5 would be pretty cheap, way faster and more up gradable for the future and you can re-use your old ram and GTX950.
The GTX950 is really not a bad card and will play all new games at pretty OK levels which can't be said of your processor.
As I said, may be easier to just sell the PC. The A8-6600 also has integrated radeon graphics, so maybe sell the PC without the GTX950?
Then, an old Dell Vostro 460/Optiplex 3020 type machine with a 3rd gen i5 can be gotten for around £120 on Ebay - throw your GTX950 into one of those and you've a way, way faster gaming PC and shouldn't really cost you any extra.