no, not necessarily. If you have a static IP address, you can just punch in the IP address itself.
If you want an SSL connection (secure), however, things become a bit more complicated.
List of what you need for a webmail program:
*) webserver (e.g. Apache)
*) mailserver with IMAP4 capabilities
*) scripting language that can access IMAP4, such as PHP or PERL
*) An actual webmail script in one of those scripting languages
*) optional: a domain name
*) optional: a ssl_module for secure connections
*) optional: a secuity certificate so that you don't have to click the warnings away