Downgrading an iPhone 4 from iOS 6 to iOS 5.1.1 using iTunes with a restore.ipsw file
In short: not if you didn't bother about jailbreaking or never heard of TinyUmbrella.

Apple is very strict on installing iOS firmware. Everytime you do a restore, iTunes is verifying the firmware for the connected device with their own server by checking SHSH blobs at Apple's servers. An app like TinyUmbrella allows you backup your SHSH blobs (they are unique for every iOS device) locally or to saurik's server. This however only works the latest iOS version that is available for your iOS device.

read this: http://www.redmondpie.com/reminder-save-your-ios-5.1.1-shsh-blobs-now-before-its-too-late/ or this: http://www.saurik.com/id/12