Yes, you could do that. However, by doing so, you essentially defeat the purpose of security because that is a backwards approach. First, the user might just choose to never change passwords. So much for private accounts if everyone knows the default password. Second, passwords stored in an otherwise unprotected BE file are visible to those who really want it.
Normally, if you are an a domain-based environment, you don't use ANY password on Access but instead, you choose to trust the user's domain login. You can ask for the help of your domain admin in creation of a group identifier and then add your intended users to the implied group. Put group permissions on the FE and BE files in the shared location. But also put a "DENY ALL" on the same files. I should note that this particular scheme, which is essentially to trust the domain management software for security, is in use by the U.S. Navy at their Navy Enterprise Data Center in New Orleans and is approved by the U.S. Dept. of Defense as a viable scheme for non-classified data.
If this is NOT a domain environment, just a "loose" network, but you still want security anyway, you would probably want to not allow access until they visit you ONCE to have you set their password. Further, note that if you were planning to encrypt the BE file, then EVERYONE needs the same password forever, because the password would be the encryption key.
Search this forum for articles on the subject of security a database. You'll find a wealth of information on the subject.
EDIT: I see Colin beat me to it. That's two of us who don't think you should store passwords in a DB BE file.