Some musicians play with this deliberately. Sigur Rós sings some or part of their songs in Hopelandic, a kind of glossolalia that vaguely resembles Icelandic. The album booklet for '( )' contained blank pages for listeners to write their own lyrics into. Elizabeth Fraser of the Cocteau Twins sings in a form of English that is almost but not quite comprehensible. And Lisa Gerard of Dead Can Dance sings pure, invented glossolalia.
https://www.youtube.com/watch?v=QJhVM930YXY
https://www.youtube.com/watch?v=dtBr5JKSuks
https://vimeo.com/3977534