Sync Mail with multiple macs with dropbox

Can this be done?

I switched from a PC to Mac and love it. I went from Outlook to Apple (Mac) Mail, calendar, and contacts because of its simplicity.

I have a 27" at work, 20" at home and 13" macbook pro for travel.

Can I sync my Mail - including sent, received (9 emails), Folders - rules (14) with my computers with Dropbox???

If so, what folders/files do I need to sync????

Once synced will, when I open my macbook pro will it be the same as on my 20" iMac at home?

Obviously I can only use 1 mail program at a time.

See image*

Thank you

PS - please don't tell me about imap or gmail/hotmail. I like the way I am managing my email and I like that they are saved on my work desktop.

Settings:
27" iMac (work) - manually receive and remove from server
20" iMac (home) - auto receive but leave message on server
13" Macbook pro (travel) - auto receive but leave message on server
iPhone - auto receive but leave on server / delete from server when deleted from iPhone (to manage spam)

If I receive at work, then I loose the mail on all other devices. (thats ok)