In a way yes.
If you have a 750GB drive and it is almost full.
Then the drive can slow down.
One of the reasons is more to do with how the data is read off the drive.
When the drive has been used a lot and data has been added or removed.
Over a long period of time the drive and files fragment.
Or scatter information over the drive randomly.
The drive slows due to the fact that the read write heads have to constantly move to retrieve chunks of data.
Most since game data is on the hard drive, read off it and passed to the graphics card or memory of it the delay can impact fps depending on the game.
I would clear some space, and if you have not de fragmented the drive for some time do so.
It will take some time as the drive is large in capacity.
So if it is heavily fragmented. your best starting a defrag before you go to bed as it can take 4 or 5 hours. or more.