Hey how ya doing .
I love Nexus phones because they are so easy to root. Also easy to get confused
So if I am understanding correctly, you want to upgrade to ICS 4.04 and still have it rooted? Well I believe there are a couple different ways to go about this.
One, yes, you are correct with your estimated guess. Create nessesary backups and return the phone to its stock state, Gingerbread 2.3.6. Then upgrade, and root. My knowledge seems to lack the power to tell you how to get the Nexus back to its stock state, sorry. But Google should be able to assist you.
The way I would do it is to find a ROM of stock ICS 4.04 online and flash that. Seems much faster to me, but I see finding that ROM as being difficult.
Let me know how you go via personal message if you need more help!
Also, a disclosure, I am not a expert when it comes to Android, so be sure to you know what you are doing before you take any risk! Best of luck.

 

Hello, philgrzyb.. welcome aboard.

I moved your thread to the Nexus (ATR) S section for it to get some faster responses.