Nope. The system sees the user address as [username]@[machine].dreamhost.com - nothing related to the domains you have. This user has a mailbox, where messages are stored as files - also nothing to do with the domains you have.
In addition, DreamHost has it setup that you control a single “primary” address for each user and you can have multiple “secondary” addresses by simply adding a forward-only address that forwards to the primary address. Of course both the primary and forward-only must be one of your domains.