How can co-authors check the status of a submitted manuscript in Elsevier Editorial System?

The answer is No, he/she cannot cannot give any permission to the co-authors after submission to EES and before acceptance, as mentioned here:

I am a co-author on the paper, I would like to be able to see the status of the manuscript. I have the manuscript number and I am registered on the journal website.

After submission, you can only see the status of a submitted paper via the corresponding author's EES homepage. You will not be able to search for this submission via your own author's EES homepage.

So just the corresponding author can check the status before acceptance. But after acceptance, co-author can track the status as well:

After acceptance, the article is recorded in our tracking system, you can use the production reference number along with the Corresponding Author's name to track your paper status and add your paper to your personal homepage on http://www.elsevier.com/trackarticle.