Will my old hard drive affect framerates ???

Not generally. All a slow hard drive usually does to games is increase load times. Once you're loaded up and running, the drive isn't doing much but maybe loading up an occasional texture or object, nothing very intensive. If you're low on texture memory and textures get swapped out to main memory and then to virtual memory, you could see a huge lag spike. Not a real likely scenario with a 6670, though.

That's actually more of an issue of hdds access times which hasn't really changed any. Even on new hdds you will see textures or objects pop. It usually doesn't affect fps but some games will pause when it's loading, most modern games will usually just have a low res texture to show. Games tend to load everything it can in the ram to prevent this as hdds being a bottleneck has always been an issue(and always will be). I'd say you don't need a new hdd but the more a hdd is used, the slower it tends to go which is an issue with reusing old hdds.