canon 5D Mark III audio question? avoiding syncing...

Hello!
thanks in advanced.
I used the H4N audio recorder plugged into the 7D hoping I wouldn't have to sync later in post. But with the auto gain audio of the 7D it wasn't good. Even if i used a rode mic (without the H4N) i would get a lot of noise most of the time.

With the 5D mark III would i have the same problem? i know now it has the levels control, better audio... etc... but could i plug the rode mic into the 5D mark iii and be good to go?
If I plug the H4N directly into the camera would i have to sync?

Thank you very much!
Leon.