Xbox – How to trigger the ascension/numbers cinematic at the beginning of Black Ops

No, there is no known relevance to anything other than the single player campaign.

Since you haven't played through the single player campaign, I won't give it away, but you can look up the meaning of the numbers here on the Call of Duty Wikia. Also, you can use the terminal in the menu (Accessed by tips in this question: How do I access the hidden mini game in Call of Duty: Black Ops?) to DECODE the numeric messages if you'd like to do it alone.

There is no co-op campaign. You can only co-op in online multi-player and Zombie mode.