I can't say for certain that it has an effect, but I can say from experience that I'm in the exact same situation (about 60gb left on my terabyte hard drive) and well... it's seen better days. Can't say for certain that's the cause; it's also about 4 years old, so...
of course it will. first off, having the OS on an hdd is already slowing your game loading/rendering/saving speeds down, having only 50gb only makes the startup and shutdown of the pc and apps much slower.