Only if you're recording footage to your storage device at the same time. If you are recording with fraps you'll see a big difference in the stuttering. Maybe if you run out of VRAM it'll start switching back and forth to the storage device for the video encoding, which will drop you to around 5-8fps with an HDD. It may be faster then, but 12fps isn't that much more playable than 7.
TL;DR If you have low VRAM or plan on using fraps often an SSD is nice, otherwise it won't make a big difference.