I use three different online calendars. One synchronises a calendar to Google Calendar. This is useful if you wish to share a calendar with an Android phone or tablet, or other instances of Thunderbird. Another synchronises with a calendar offered by one of my email providers, using CalDav. The third uses Dropbox to store an ics file. This is probably closest to what you ask for. The file on Dropbox is also available to other instances of Thunderbird, so it is both a backup and a share. You just install your calendar as a network calendar, using the file:// protocol to link it to an ics file. However it is not a true share and I think it could go horribly wrong if two instances of Thunderbird were to access it simultaneously.