I don't think we necessarily need to wait. We have studies on their vocal bone being larger, and more forward set. This alone would produce weird noises. Then we have studied their DNA compared to ours such as methylation associated with the vocal chords and face. These levels show the level of production and development of these features. In Denisovan and Neanderthal these are significantly lower than modern humans. Even lower than Dolphin/Wales, capable of limited vocal communication. There isn't actually much difference from a Chimpanzee and Denisovan and Neanderthal in this body development.
I think beyond basic grunting communication or very low level vocalization, Neanderthal were mainly suggestive communicators. Pointing out things, hand language, etc.