> Can Mail.com Emails be downloaded? 

I really have no idea - your can check various related 
threads (search for yahoo groups here) at httrack.com, 
however

> If yes, then how?
Using ADD URL/Capture URL, and by capturing the login page. 
Then, you will need to define filters (Set Options/Scan 
rules) to get exactly what you need ; such as:

-* +www.example.com/readmail* +*.gif +*.jpg +*.png +*.css 
+*.js

This may work, if the site is not too complex and if you 
manage to detect what type of link has to be downloaded.