I’m all googled-up with my own address, drive etc running on all my devices.
Is there a way I can access this document without logging out of google each time I want to look at the document (which will be frequently)?
could they not just share the doc with you? as opposed to giving you their account details?
Yes open the docs and share it with your account by clicking the big blue "Share" button on top right.
You could always just open a chrome incognito window to log in as the second user.
The incognito session knows nothing of your normal chrome browser details or sessions.
Nothing is impossible for the man who doesn't have to do it himself - A. H. Weiler