hMail only runs on Windows. If your shared host is Windows, it may work. You may want to contact the hoster to verify that running a public mailserver is allowed under their ToS.
Just to make clear - Roundcube is a web-based IMAP client. Other than being web-based, it is no different than any other IMAP client such as Thunderbird, Outlook, etc. Roundcube can not send or receive mail all by itself any more than Thunderbird can. All clients need a mailserver to do the real mail work.