No you won't - to re-iterate, the drive speed affects loading times only. So unless your game is loading stuff during gameplay (most games don't, or don't much) gameplay will not be affected. It's GPU power that dictates frame rates, and that in turn is affected by how well balanced your system is overall, ie you need RAM, CPU, mobo suffiient to get the most from your graphics card.
All that said, if you have a Samsung 850 SSD, use that as your OS drive (and make sure to enable rapid mode in Samsung Magician) and hopefully you'll have enough space to install your favorite games of the moment on it as well