Yes it's possible to use unlimited hosting companies to manage your client's websites and still provide them basic FTP, MySQL, and Email access.
Once you have added your clients domain to your account as an addon domain. You can create FTP accounts in your control panel, even if you must use your primary domain to generate the accounts such as firstname.lastname@example.org, you can tell your client to use email@example.com as the login and it will still work. Test this to see for yourself.
MySQL you will most likely need to allow remote access. Ask your client for their IP, do a reverse DNS and use the name version such as *.clientISP.com to give remote access. If you specify their exact IP and they are on a DHCP connection and the IP changes it can cause some delays for them. So to avoid that just use a wild card for their IP's reverse DNS domain. This is often different than the ISP's corporate domain so check.
Email you can typically tell them to login to http://mail.clientdomain.com and they'll be able to access their email as well as change their password. You'll probably have to provide them the pop3 and Imap information though once you create their emails.