How can I synchronize old notes with an email account on the iPhone?
Syncing the notes to your computer, then moving the notes to your email notes and letting it sync back to the phone would be the easiest.

Without syncing you could email each note to yourself by clicking the envelope icon at the bottom of each note. Then turn it into a note in your email account, of course this would take a long time but you wouldn't have to sync with your computer.