I know it is possible for several users to access a database at the same time for viewing purposes, but is it possible for several users to be
in the database at the same time entering data into a form to update a table?
Yes, it is possible. As long as they aren't trying to update the same record at the same time, they will generally be able to update different records, even if in the same table, at the same time. Access will "lock" records that are being edited, so other users cannot edit them at the same time, thus preventing conflicts.