Migrate users from a custom application DB into Drupal
Yes. The Migrate module does exactly just that.

You just need to write a migration script, which is comprised of the source (there's a lot of plugins out of the box like MySQL, CSV, JSON), the destination (there's already a User class you can extend from), and the mapping (the mapping of source fields to destination fields).

Drupal will probably have a different hashing mechanism that your CMS, so the passwords probably cannot be reused. The values can be copied as is, and just force your users to reset their passwords. There's also the Force Password Change module for that.