Yes - the way I like to explain it on occasion is that "tongues" are not gibberish - gibberish does not try to mimic real language; glossolalia does.
The "non-cognitive" part of the term "non-cognitive non-language utterance" (NC-NLU) is, as I mentioned, perhaps a bit of a misnomer. I tend to think that the person who coined the term (not me) meant it in the sense that either the speaker isn't really consciously thinking about what s/he is producing, and/or the language producing centers of the brain aren't going to be used all that much in its production (as the often quoted Univ. of Penn. study done several years ago demonstrated). In a way, it's a bit like when you blink your eyes during the normal course of a day; there's no real conscious thought process involved - it's just done. In that sense it can be said to be essentially a "non-cognitive" process. I think that's the gist of the "NC" part of NC-NLU.
I do agree with what you say further above. Yes, definitely - for some 'speakers' it is initially a very cognitive process as they "learn" to speak in 'tongues'. Once they kind of 'get the hang of it', it becomes essentially a non-cognitive (as described above) process.