Here's the official response I got from EA:
Greetings,
Thank you for contacting Electronic Arts.
I appreciate your interest in EA games.
However, regarding your issue, please allow me to share that as you have been already informed that you will not be able to register your copy of Mass Effect 3 without an Xbox Live Membership. So, I request you to register your gamertag with the EA account and then try to play the game.
I hope the above information helps.
We at Electronic Arts appreciate your efforts and involvement in our Games and take this opportunity to express our gratitude and extend support throughout. Please feel free to get in touch with us anytime. Also, please access our online knowledgebase on:
http://help.ea.com/
Regards,
Rohan
Electronic Arts – World Wide Customer Experience
For those who DO have Xbox LIVE or PSN Network Memberships, you CAN contact EA via chat and they WILL link your accounts for you (or so I was told). Chat is the best way to contact them. My wait time was usually under 3 minutes.
Go to:
https://help.ea.com/ and click on [Talk to a Game Advisor].
For those of us that play offline, looks like well have to take our case to Bioware, eh?