So I have a stupidly vague understanding of CHIM, but as far as I can gather, it's a person in TES who realizes that they are just a part of a dream of an immensely greater creature or entity, even the Divines and Daedra are part of this dream, and probably not even real. They use this knowledge to 'lucid dream' and change the universe around them at will.

Well, if mortals have wielded this power, could a Daedra? And what would the repercussions be? If Daedra are already all-powerful in their realms, immortal and have limitless potential to change the world around them, what would happen if a Daedra achieved CHIM? What could they do differently? Or are they already experiencing CHIM, and that's where their power came from?

I don't know, this may sound silly, but I'm intrigued...

This question may as well extend to the Divines. I know that (apparently) Tiber Septim used CHIM to become Talos, but what would a god do with such power if their hold on the mortal world is tenuous at best? Again, are they as powerful as they are because of CHIM?

The way I understand it, et'Ada can't attain CHIM because they're too "big". They're still too much idea and not enough person to really understand the concept of individuality. Lorkhan tried it and failed. Mundus is The result of this failure.

I don't think its right to say Daedra can't achieve CHIM. Its presented as though Lorkhan could have done it, but failed on purpose. If any Daedra have/will have CHIM, my bets are on Dagon (Commentaries) and Mora.

But for what its worth, Vivec apparently learned it from Molag Bal:

Although that could be interpreted to mean literally the word, not the state.

Lorkhan is different from the Daedra. He discovered the Tower and became obsessed with it because it was his nature, being the unstable mutant that wanted all of creation yet none of it. The Daedra discovered the Void but their nature didn't allow them to recognize the significance of the Tower.

Mora surely knows of CHIM, and stashed that knowledge into a shelf somewhere, because that is his nature. To collect knowledge, not to use it.

Dagon's nature is destruction. The desire to tear apart the world until Alduin is satisfied and lifts his curse on him. As Divayth Fyr put it, http://www.uesp.net/wiki/Lore:Varieties_of_Daedra.

You said Daedra can't achieve CHIM because they are "too high up." I was just pointing out that that's wrong. If you want to argue that they won't achieve it because of particular features of their nature, fine. But predicting that someone won't is different from saying they are actually unable to.

With Dagon you seem to be ignoring the Mysterium Xaraxes.

Molag Bal you didn't mention at all.

EDIT:

Also, Lorkhan is different from Daedra now. Daedra are "not ancestors" while Lorkhan is an Ancesotr (ie. Aedra.) But prior to creation, he was simply a Padomaic et'ada, same as any current Daedra.

The Daedra being too high up is the reason why they are bound by their nature. To understand the meaning of "I" you need to encompass nothing but yourself. Not be an idea but a person. Therefore being unable because of position and being unable because of nature are the same, but I should've properly said that earlier. I've got the annoying habit of throwing out random ideas without proper explanation. Already back in school drove my literature teacher was driven crazy by this.

The reason for Lorkhan being different has nothing to do with Aedra/ Daedra, but nature. Lorkhan is the one et'Ada closest to Sithis. The idea that everything is nothing is one is everything is written in his very being. He had to become obsessed with the Tower, just as Mora has to be obsessed about getting his tentacles on a new secret knowledge.

I'm not ignoring the Mysterium, but Fyr also say that Dagon not only knows and understands nothing, he also talks freely and without falsehood. He's the type to write a book out of stuff he heard but not understood and hand it to his crazy cult leader who doesn't understand it any more.

To Molag Bal I unfortunately can't say much. But my subjective impression of him is that his nature is incompatible with CHIM as well. As the Lord of Domination he'd naturally put himself over that which he seeks to dominate, and being above everything else doesn't mix well with the idea that everything is one.