The answer to your main question is contained in VIRTUAL_README
all offer through the database, as that without it no
Absolutely no database in any way. Should Postfix somewhere to take addresses and passwords of users? But what would it be for the SQL — database, LDAP or flat files — is another question.
PS From your question it is unclear at what stage of setup Postfix you have any issues with adding domains. Whether the question more specific, perhaps, and the answer was not so common.