Anecdotally, when I was an undergrad, one of my professors mentioned having seen a study or two on glossolalia. The studies indicated that the phoneme inventory was always quite small, smaller than that found in practically any natural language. Maybe even smaller than the Hawaiian inventory of thirteen phonemes, although my professor didn't go into details.
My professor was an excellent linguist. She did believe that glossolalia was, at least in some cases, an inspired state and that people in that state were often speaking genuine languages. However, they weren't natural human languages.
Goodman, Felicitas (1969). Phonetic Analysis of Glossolalia in Four Cultural Settings. Journal for the Scientific Study of Religion
227-239. Goodman, Felicitas (1972). Speaking in Tongues. A Cross-Cultural Study of Glossolalia. The University of Chicago Press. Samarin, William (1972a). Tongues of Men and Angels. The Religious Language of Pentecostalism. The Macmillan Company. Samarin, William (1972b). Variation and Variables in Religious Glossolalia. Language in Society 1:121-130. Samarin, William (1973). Glossolalia as Regressive Speech. Language and Speech 16:77-89. Samarin, William (1974). Review of Goodman (1972). Language 5:207-213.
Malony H.N. & Lovekin A.A. 1985. Glossolalia, New York, Oxford University Press.
Dilia Flores. Analisis y Comparacian de Hablas Sagradas en Tres Formas de Trance-Posesian: Un Estudio en Etnografia de la Comunicacion. Universidad del Zulia, 1987. A study of glossolalia and related phenomena in Maracaibo, Venezuela.
_Tongue Speaking_, Morton Kelsey (New York: Crossroad, 1981).
_They Speak With Other Tongues_, by John L. Sherrill (Westwood, New Jersey: Fleming H. Revell, 1964), a popular treatment.
_The Pentecostal Movement in the Catholic Church_ by Edward D. O'Connor (Notre Dame, Indiana: Ave Maria Press, 1971) claims cases of xenolalia (speaking in an unlearned, existing language).
And a recommendation to perform a library search for Donald Clarence Laycock which might uncover a few things on glossolalia.
There are literally 30 Well Known LINGUIST claiming Speaking in Tongues is a REAL LANGUAGE, but not a Human Language!