No, PEAR isn't going to magically solve these problems for you.
PEAR is a collection of PHP classes that are meant to solve common problems faced by PHP users. The Mail packages offer code for interacting with different parts Email systems. They do not contain code for creating email systems from scratch.
For example, form the Mail_Queue documentation
The Mail_Queue class puts mails in a temporary container, waiting to be fed to the MTA (Mail >Transport Agent), and sends them later (e.g. a certain amount of mails every few minutes) by >crontab or in other way.
The MTA in this case in sendmail, postfix, etc.
Another example, from the Mail_Mbox documentation
It can split messages inside a Mbox, return the number of messages, return,
update or remove an specific message or add a message on the Mbox
Incorrect use of "an" aside, you are using this to read existing MBOX files, and not caring how they got there.
The Mail package is about interacting with existing mail systems, NOT creating replacements. You'll still need to understand how all those email systems work to create a "full mail server, similar to a conventional SMTP mail service". If you're doing this because you want to learn how email systems work, have at it. If you're doing this because you thing this will give your business some leg up in the email game, I laugh and say "good luck with that"