This is your call, but I don't recommend anyone use Google Docs for their sole copy of any important work. As a former professional genealogist, I got a peek into some very scary analysis of "the cloud" done by an organisation trying to assess the safety of data stored in such a fashion. As someone who already leaned toward the cautious in such matters, I was shocked when my worst fears sounded like Pollyanna next to the huge doubts this white paper raised. Sadly, it isn't public, since it can be risky to publish an honest analysis of anything other people are making billions from. But I got a copy of the paper back channel from somebody who worked for large 'stakeholder' in genealogical data with very good reason to want to know the truth.
And even if you chose to store documents in the cloud anyway, Google wouldn't be my first choice, or even my third. Look at the e-mail outage today. Sure, they usually get back most of the data, sometimes even all. But they have lost data, which might not matter so much when it was just an e-mail. But if it's your manuscript, losing just one day's work can be a disaster. (At least, I'd find it so.)