Yes, however users will run into Microsoft known limits:
1) If a user with read-only access views an .mdb in ArcMap first, and a full-permissions user opens it second, the second user will not be able to edit the Personal Geodatabase. All users will be able to read the document only.
2) If a user with full permissions to the .mdb views it first, any users with read-only privileges cannot view the .mdb at all. Other full-permissions users will be able to view the document, but only one such user can be in an edit session with the same .mdb at any one time.
Personal geodatabases will have these limitations in multi-user environments. In order to have many users view and edit the same geodatabase without affecting each other, use an enterprise geodatabase in ArcSDE.