Hi aghilmort,
As long as you don't click the links to re-authorize your Google Drive connection on the UD settings page, then being logged in to a WP account whilst also logged into Google should not affect anything. UD doesn't have any other code that touches the access tokens. It is possible for the access tokens to be expired from Google's end - I don't have any particular knowledge on when/why that happens... if your searches turn up anything on that, then I'd be interested to learn more about it. I've not seen any of the sites I backup into Google Drive require re-authentication yet. Perhaps Google have some automated algorithm that expires your tokens if they get suspicious - but this is pure guesswork. We've not been asked this question much before, so my hunch would be that it's not a generic thing.
You don't need to have a unique Google account for each backup, but you do need to have a unique client ID - as mentioned on the UD settings page in the GD section ("N.B. If you install UpdraftPlus on several WordPress sites, then you cannot re-use your client ID; you must create a new one from your Google API console for each site.").
Are you a Premium customer? If you are, then please do use the support facilities at updrafplus.com - the wordpress.org rules don't allow us to use these forums for supporting paying customers. If you're not, then please do take a look at Premium... it's the revenue from people who are using UD professionally that enables us to offer the product and support for anyone.
Best wishes,
David