I have played a chiv/archer/tamer for a long time but I do have vet on the char as well. Yes, the Cu will try to keep you healed but, if it is taking damage it generally worries about healing it's self first. Cu's are only ok (at best) as tanks really, especially since the Greater Dragon has hit.
Also, I found having just chiv to try and keep pets healed was not too effective honestly.