I have found a demo on the net that is labeled as the Uruk-Hai demo. It has 6 songs (untitled). I have heard from different sources that Uruk-Hai never recorded anything, and at others that this is indeed a real recording. Is it possible that this is really an Ildjarn demo? Because I know that several Ildjarn demos have been bootlegged as Burzum.

I'm fairly certain that the Ujkuk-Hai "demo" (and I do believe that I have actually heard part of it) is just the Ildjarn "Unknown Truths" demo with ambient pieces thrown into the beginning of each song. They even have the same number of tracks.
I love that Ildjarn demo and identified the Uruk-Hai "demo" as it as soon as the metal part began

According an old interview in German Ablaze zine, it was just a once-in-a-lifetime rehearsal, which ended in serious boozing. Nothing was recorded there.