If I'm an Apple iOS developer, can I do iOS upgrades, downgrades within the registered devices?
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.