Android upgrades

One day, probably in '13, I will buy a smart phone. I have some Android questions...

Is it true that if Google releases an Android update, you're pretty much at the mercy of your carrier when you can install that update, if your hardware supports the update, and if your phone is not rooted (or you don't own a Nexus device)? Also, to what extent do different carriers & phone manufacturers add or remove to the UI relative to the pure Android UI? Does anyone make a more functional/enjoyable UI than Google?