Yes, the messages from iMessage are synced when you put the Caller ID on the phone to your email address associated with your iPad (and Apple ID). The iPad only uses an email address for it's "Caller ID" so in essence, that is the limiting factor. The iPhone can use as a caller ID either an email address or a phone number. However, you have to set your phone to having a caller ID as the email address in order for the messages to sync.
One downside to all of this is that when you get the devices synced, if someone sends you an iMessage, BOTH devices will alert you at the same time. It's a bit startling to have your phone and iPad beeping at the same time! However, you can answer from either one. Same applies to Facetime calls.