Your storage won't affect the performance you get in games at all. Frame rates for example won't change a single bit.
What will change is level load times and the length at which it takes to complete the initial install after you've downloaded the game.
Everything else relating to the game such as textures, will be held in either GPU memory or system memory when it runs out.
Both of these are much faster than an SSD or a mechanical hard drive.
(It's very rare that a game will save what it's holding to the storage medium. And, it will retrieve all the data it needs from the storage medium before the content appears - Ie, load screens).
In short, it's fine - Putting your OS on an SSD and everything else on a storage drive...