Yes, the Corsair CX 500W power supply can indeed power an FX8350 with either a GTX 950 or an R7 370. Would I recommend it? Not at all.
For one thing, the quality of the power supply is not very high. In terms of its internal components, it uses capacitors made by Samxon mostly, whereas Japanese are always the best. Corsair CX capacitors are known to die rather quickly, and this unit will be strained quite high with your components. Secondly, it does not have the best voltage regulation nor ripple suppression - long story short, you want your power supply to output as close as possible to the correct voltage of electricity, and while Corsair CX is in these requirements, better power supplies with safer voltages and ripple can be found.
Lastly, Corsair CX 500W is labeled at 30C. You computer, and this power supply, will be hotter than 30W. Transistors have a property called derating, so as their temperature increases, they lose their ability to transfer as much electrical current. So wattages will actually be quite lower than as labelled on the supply.
I would buy an XFX 550W unit. More money? Yes. Worth it? You bet.