i think to do this you need to play with 4 friends who all agree to play the role. i think if you do this in HC it will work better as people will have a better reason to stick to the plan
can it work? i say without a doubt. not sure if its the best bet though. you can probably build a "tank" with some damage anyway. same with healer monk.
do you have friends getting the game also?
Healer monk would need to do damage to generate healing, anyway. I think that this sort of team synergy would work best with dedicated "pros" who regularly game together and use their "roles" as secondary to their damage dealing abilities. So the healer monk would really be DPS, off-heal. The tank barb would be DPS, off-tank. And they will all want crowd-control, I am sure. So really, what's the point of roles again? I think I just talked myself out of it...
I think tactical unit cohesion (situational awareness, communication, information dissemination, optimal ability use, etc.) will be infinitely more important than role.
Edit: Sorry. I don't mean to downplay what the OP would find fun. I am looking at this from a clinical perspective of optimizing cooperative gaming ability.
I edited my post with a few monk skills that might be used for healing, after looking them up.
I just want to clarify... This thread was meant as a way of discussion on what people think about what will be more viable. It does not necessarily represent what I personally think is fun or want to do. To those that understood that and gave good comments, thanks for all the input.