If I'm an Apple iOS developer, can I do iOS upgrades, downgrades within the registered devices? I have an iPad 2 GSM with iOS 4.3.5 that I would like to upgrade to iOS 5.1.1. 

I tried to upgrade using an Apple 5.1.1 image, without success due to the signing window for 5.1.1 being closed.

If I enroll in the Apple Developer program ($$$) will it be possible for me to upgrade to iOS 5.1.1? How about downgrade to other versions (e.g. 4.1)?
No, being enrolled within the Apple Developer's Program does not provide you with any kind of special downgrade possibilities. 

In the other hand, being a Developer grants you the ability to upgrade to the newest yet-to-be-released version of iOS. 

So, being the iPad 2 eligible for iOS 6, you won't be able to upgrade it to iOS 5.1.1 instead, enrolled as a Developer or not.