Examining other languages for a look at laryngeal activity
The Tuva of central Asia have a style of singing that involves the false vocal folds as well as the true vocal folds. Their singing has more than one fundamental frequency. You can watch a 1-minute video of this here.
Another way to find out how laryngeal activity in speech works is by looking at tone languages. In English, pitch and intonation affect pragmatics, but in Mandarin Chinese, these are phonemic. In English, pitch is non-phonemic, and is used in suprasegmental features like intonation and prosody. Intonation and prosody don't affect the identity of the phonemes, but they can affect meaning. An example is the phrase "You will go" with different intonations. Pitch carries information about the speaker, rather than the content of what the speaker says. You can see the emotional status of the speaker through pitch.
In Mandarin, the different levels of pitch are phonemic. For example, the syllable "ma" said with a high tone is "mother." Say the syllable with a high rising tone, and you have "hemp." Say the syllable with a low dipping tone and you have "horse." Finally, say it with a high falling tone and it means "to scold."