Unlocking and restoring aren't the same thing. You can get the old ipsw files for free on iclarified. This has nothing to do with the problem. The problem is related to apple signing the restore, which they won't do. Downgrading requires shsh blobs specific to your device and the iOS version. These must be acquired while apple was still signing restores of that specific iOS version. Additionally, the restoring software requires a hack of sorts to get the phone to respond to the shsh blobs. This doesn't exist for the 4s while downgrading from ios6, at least to this point.
The answer remains no. Jailbreaking is irrelevant to the question.
This has been by far the most helpful post. Thanks for explaining that, I think I'll keep away from jail breaking for now just incase anything goes wrong and I need to updating to sort the problems out, risking wifi problems.
BTW, do you know whether Apple have sorted out the wifi bugs?