Nope. I've joined the Companions for four of my five different characters (one is a mage and has no need for melee weapons; hence, no joining a warrior's guild), and all of the times Farkas has still been tagged as essential after Glory of the Dead. He's fallen from cliffs half the height of the Throat of the World and lived. Enemies have used Finisher Moves on him and he was still living. Four Pyromancers surrounded him once with spells that nearly killed me and he didn't die (but his brother did from the same circumstance on another occasion), and Forsworn Briarhearts have done innumerable Power Attacks to him (which are basically deadly to everyone else) and he only got down on a knee but then got up again later.
'Nuff said.