They can work and they might work very well provided any and all axes are left outside as it were.
In other words, how do we know that the opinions that are given are constructive and are not embued with any negativity?
Can we be absolutely positive that those offering criticim are able to be fair? What if they aren't able to be and they don't realize it? Maybe they just don't like stories about vampires or even if they are sworn to adore every single story about vampires (or whatever it is you write about) they just don't like our story. Or even worse, they don't like us?
I believe in the 'ideal reader' that Stephen King speaks of. That is absolutely beyond doubt. However frankly I don't like critique groups. I have no problem however with workshops that offer critiques. Face to face workshops where we can discuss things one to one. That's fine as are critique groups that are also face to face.
I joined a wonderful workshop ten years ago for a time. I hadn't written since I was a teenager and that workshop was the very best thing that could have happened to me. I was enouraged, inspired and critiqued too. I learned in a constructive atmosphere and I learned happily. I don't belong to any now because at the stage I'm in now I feel it would paralyze my writing. My ideas would die before they ever saw the light of day.
But here's another point of mine, as for critiquing in general, I don't like showing a story or a novel (especially an unfinished-barely begun novel) for scrutiny. It's like having a ten day old fetus adjudged for its viablity. IT'S TOO SOON, PEOPLE! The little embryonic bunch of words will not go full-term. It will die before it is drawn forth, before it is allowed to gasp its first breath...!
Okay, I'm getting carried away, sorry.
Answering this question on a purely subjective level: no. Critique groups do not work for me, I am not comfortable. I have to have my story grow and become whatever it becomes.
Possibly the reason for this is also that I am a 'seat of the panster.' I know my characters, have a basic idea of the plot and go for it. I get zero draft done first, then a proper first draft. Now since the zero draft is just that: ZERO, how can I ask anyone what they think of it? I can bounce an idea off someone, that's different but for critiquing, not for me I'm afraid.
Having said that what works for me may not work for another. No one ever lost anything by trying a critique group to see if they liked it, if they could benefit from it.
Nothing in life is certain nor is anything written in stone. With regard to writing, there are no rules. Writing is a great journey and if you find a vessel to sail the stormy seas in that is right for you, climb aboard, set your sail and seek your dream!