I'm no psycholinguist (although I'm reliably informed that as linguists go, I'm pretty damned psycho), so I don't know how common this phenomenon is. It happens every once in a while I'm right on the edge of either falling asleep or waking up: I get running through my head a perfect nonsensical parody of English prose. Glossolalia is probably the closest word I can come up with, but I don't speak this gibberish, as in "true" glossolalia, but I do think it. But of course, the instant that I realize it's happening, it stops. Thinking about not thinking -- you understand. The Buddha would have trenchant things to say. James Joyce, too, come to think of it.
Well, what's funny about it is that some nutty MIT students have created a computer program that generates scientific-academic gibberish that's so good that it was used to gin up a paper that was accepted by the Ninth World Multi-Conference on Systemics, Cybernetics and Informatics. The conference organizers later withdrew their invitation after the hoax was exposed.
Give it a try.
Read the resulting gobbledegook out loud to yourself. That's a very good simulacrum of what it's like to be inside my head at 6AM.
(That is, when I'm not thinking about sex. The Buddha would have something to say on that, too, I imagine.)