No, you do not. I have the basic free yahoo account and push my emails to my phone just fine. In many cases, my phone receives the emails before my yahoo account does that I have up and running.
I do have issues with syncing contacts because the fields in yahoo are not all the same as with the phone. Many times yahoo will have a contact info as "home" while after the sync the phone will have it listed as "work." I can't get fax numbers from phone to sync to yahoo either. Very frustrating!