Anything is possible, but anything beyond the simplest screen scraping (fetching a series of linked pages, preserving login credentials, cookies, etc) in shell is going to be rather painful. The shell is good at passing simple textual data between different tools, but this basically calls for a tool which preserves internal state, so a scripting language with networking support etc would probably be more appropriate for anything a little bit more sophisticated.

It would help if you could provide some details. Do you simply want to fetch a list of the top Subject lines in the inbox, or actually do some real manipulation of those messages?