Yes (well previously) if I excluded a too big site, the backups worked.
In the last version of Virtualmin (or its default template) with 2 lists instead of a multiselect excluding a site does not work anymore (see my other bug report).
I don’t think it has something to do with quotas. The fact that there is not enough disk space is indeed correct. The error handling and the error message if that happens during a backup are imho incorrect and a bug.