I like the fact that a Microsoft Access .mdb file contains a complete database in a single file, so for example foo.mdb may contain all the data, table structures and queries for one database.
I want to move over to MySQL. I understand that MySQL can use many file structures. Can MySQL replicate the single file model of one database = one file?
Short answer: no.
Long answer: it depends on the storage engine.
All dbs managed by innodb storage engine are stored in one file. If you have 3 innodb dbs on the server, they all are going to be stored in one file. This can be changed however with innodb_file_per_table
MYISAM storage engine stores each table of the db in two separate files: data and index.
Why do you need a single file anyway? MySQL has a built-in replication mechanism, you shouldn’t worry about that.