Is it possible to access my tabs and collections saved to Tabox from my mobile device perhaps through Google Drive?
Unfortunately no, it is not possible to access collection data from mobile, as Tabox uses a special hidden system folder in your Google Drive to store its settings and collections.
Also, it saves that information as a JSON file so you would have to do a bit of digging around to find the URLs.
If you want, you can export your collection(s) to a text file and send it to your mobile device (email / file transfer / air drop.... )
Hope this helps!