Central Management Server - can it manage itself?
I had also previously assumed that this wasn't possible at all, until I started playing around with it.

From what I can tell, the matching is only done by the server network name that's entered.

If you attempt to add a server to the tree with the same network name, it won't allow it; however, if you use a different network name, even though it may point to the same instance, it does work.

For example, I successfully registered my local instance .\SQL2008R2DEV as a CMS, and then successfully registered (local)\SQL2008R2DEV in the tree. (Tested in 2012 Management Studio.)

From a management perspective, this may or may not be a good idea. Furthermore, if Microsoft decides to tighten down the policy, any reliance on this ability will force you to change your process.

Certainly if SQL1 would be a production instance in your case, this is a bad idea because you want to separate management duties from serving user data duties. I strongly recommend using a separate instance of SQL Server just for CMS purposes, particularly in a production environment.