I went to bed last night, and lay there having insomnia. No obvious cause: no persistent thought or worry running around my head, no physical discomfort. I just lay there, fully awake, failing to naturally descend into sleep.
I lay there all night, in fact, watching the clock gradually advance from 1:30 to 7:30. Then, rather to my surprise, at 7:30 I woke up from what felt like a deep sleep.
So I can only guess that some of that insomnia was actually a dream of insomnia; but I have no way of judging how much. In other words, I have no idea how much sleep I got last night. A sort of Schrödinger's Snooze, I suppose.
(I can't even gauge it by how tired I feel now, because what usually happens when I don't get enough sleep is that I feel perfectly fine and awake for part of the day and then suddenly become sleepy later on. So if that happens, I suppose, I'll be able to make a decent guess.)
Part of the problem is that in half-awake states I expect that my sense of the passage of time is even/far worse than normal, so as you say it's a very unquantifiable sleep.