You can share the document with any email address. The recipient will receive a notification with a link to the document.
When they browse to the document they will b required to sign up for the service. They don't ever have to use the gmail address which is provided if they don't want to but their user name becomes their login.
This is the way most websites -including Askaboutmoney- work: you sign up and you are given/choose a username before you can contribute.
That's the best answer I can offer you!
Hope this helps.
I am an IT trainer and I have run Google Apps / Google Docs training among other topics - a great suite of tools but not the only ones to provide shared documents.