Hmmm... possible, yes.
Note that MySQL doesn't matter, as DA doesn't touch MySQL during User creation, so no MySQL account can be changed anyway (no DB is created)
However, DB creation afterwards does add the User account.. and needs to match the User pass as the session password is used for various scenarios, eg: DA uses it for downloads/restores with restricted permissions (restores as da_admin is not secure, so DA doesn't do it)
For Mail, it must match the DA password, because dovecot uses the system account in /etc/shadow, so if it was different, that would also affect the DA login.
Same for ssh, as that checks /etc/passwd.
The only real viable different password would be ftp...
There was a recent request to actually have the ability to delete the system account, which I was considering adding... (if it's manually delete from /etc/proftpd.passwd, DA does hide it in the ftp page)
It might be simplest to give a directadmin.conf option not to create any system ftp account, and they can create one if they want, with some other password.
Although, there isn't much stopping the User from using the same password again when adding it.. unless DA actually forces a different value, which would probably also annoy clients...