You can try it... the worst thing that can happen is it won't work, and you'll have to restore and set up as new using 6.1.3 via iTunes.
Shame on you. Given his current situation, that's not the worst.
Dazwon, you mention shsh blobs. They wouldn't have helped. Shsh blobs are specific to the device. Otherwise there would be plenty of places to download working blobs. Don't give yourself a hard time about not having them.
As you've read, you'd need these to even begin to try the 6.1.2 install.
You essentially have two options: upgrade to 6.1.3 and lose the jailbreak or remain at 5.1.1 and wait until a newer iOS is released and jailbroken. It's unlikely you'll see another jailbreak before ios7.
Your best bet is to look at the tweaks you used while jailbroken and compare them against the changes from iOS5 to ios6. Whichever features mean more to you should dictate which option you choose.
Outside of a jailbreak window, you should NEVER blindly try setting that takes you from a jailbroken iOS to a likely restore. Anyone that suggests otherwise simply doesn't understand iOS.