This is something I was actually thinking of yesterday while driving around, trying to reproduce a vocal sound similar to that of Demilich. I found two possible ways to do it and listening to the recordings backs up my guesses:
1. The vocalist (which I'll call "he") is pitching is voice in such a low register that the "croaking" noise results from the near-bottomed out frequency. I can achieve a similar effect by opening my throat and slowly pushing air out, but it is a very quiet noise.
2. He swallows air in gulps, and then constricts his throat just enough to shape vowels, then releases the air from his stomach. This is easy to do but not for extended syllables (like the end of the 1st verse in "You'll Remain". Some joke band called Los Fecal Coproboys made some videos using the same effect. It is essentially belching words.
Now if you listen to most any Demilich track closely, you can hear a distinct sort of "click" about half a measure before any vocals start up. This could mean that the vocalist is using technique 1, in which case the click could just be him opening his lips very near the microphone (which makes sense if he, like me, can only get a very quiet low-pitched gurgle from the lungs). Or, it could also mean that he's using technique 2; if you know how to swallow air, you know that it makes quite a bit of extra noise in thee throat while the air is being forced down the esophagus, so that little clicking noise could be him taking in a huge gulp that he can carefully mete out to complete his lines.
If it isn't either of these techniques, them demon possession is my next guess.