not all messages, but messages sent to your e-mail can be. Anything sent to your mobile number will only appear on your phone.
If you want e-mail messages sync'd, you need to go on your phone, go to settings, messages and make sure that iMessage is enabled, set to receive messages at your mobile number and e-mail. Now anytime an iMessage is sent to your email it will appear on any iPad, iPod Touch, iPhone, or Mac associated with that address.
If you change your Caller ID to your e-mail, any time you send a message from your phone it will be sent from (and consequently replied to) your e-mail (thus appearing on all devices)