The message will say "You have angered the Beast" (Standard anger message).
But because your Honored, NOTHING that is NOT ALREADY aggro'd on you will go to the aggro state. Meaning nothing will attack you.
You ask if it bypass's ... I would say it prevents any non aggro'd mob from taking any aggressive action as long as the Honored Flag is set. Any Aggro'd mob will be excluded (can only happen because the mob was aggro'd on you before you honored yourself, thus will remain aggro'd after you honor yourself).
Once the Honor expires, it will turn gray, it will turn on you, it will kill you.
There is a 5 Minute Cool Down timer on the ability to Honor Yourself.
Select your target, Invis, Honor yourself, get cose and cozzy to the target and spam the daylights of a tame last target (better be the Pet to be) hotkey.
To try to be a bit clearer.
Mob A is aggro'd (Aggro = attacking) on you.
Mob B is NOT aggro'd.
You Honor yourself.
Mob A stays Aggro'd on you.
Mob B will NOT become aggro'd until Honor has expired.
How to get Mob A off you ... Invis, hide what ever. Now Mob A is no longer aggro and will not go to the aggro state until Honor has expired.