The short answer is no. Smart mailboxes are basically filters. All mail is still in the original mailbox. Or as Apple puts it:
A Smart Mailbox shows in one location messages that are stored in other mailboxes. For example, a Smart Mailbox might show all messages from a specific sender or with a certain type of attachment, regardless of the mailbox where they’re stored.
You could however create your own sort of smart mailboxes by using rules to move messages around based on certain characteristics. https://support.apple.com/guide/mail/use-rules-to-manage-emails-you-receive-mlhlp1017/mac.
First create your folders. In this example I created "Today" and "Archive":
Then go to Settings and create rules.
Example of rules creating a Today folder:
This moves all mail of less than a day old to the folder called Today.
The second rule moves all day more than a day old to a folder called archive. This should give you an idea how to work with rules and folders.