Yes they should, that's the point of healers. If you couldn't stop someone from dying with your heals, healing would be pointless. As a damage, you need to Target the healer first. Once you cut off the enemies healing, they'll either die, or have to run away from the OBJ to avoid death.
I'm gonna have to disagree with role lock. I like the idea of it, but it mainly comes down to toxicity. Say you're too slow and are the last to pick, and the only thing left is support, and you don't play support. In fact, you hate support. What do you do? You just leave the game and put your team at a disadvantage. But, you don't want to take the penalty for leaving a match. So what now? Simple, you just throw the game. You don't heal (probably because you didn't want to heal in the first place), you barely fight because you know you'll probably lose most encounters because you don't play any support characters, and you're just overall a detriment to your team. It'll happen way more often than people think. People throw games because they don't get the character they want, let alone not getting the role they want.
Personally, I have no problem with taking Daemon in a 1v1. It may just be that I one trick Nid, and he seems a good counter to Daemon.