Is saraswati nadi involved in mantra practice?

By association, yes. It is the channel of the tongue, and chanting is the practice that most directly involves it.

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Secondary channel

Saraswati

Sarasvatī · सरस्वती

Running parallel to sushumna and ending at the tongue. Named for the goddess of speech, learning and music, and treated in the texts as the channel behind clear articulation.

tongue speech learning

Runs: Parallel to the central channel
Ends at: The tongue
Name means: The flowing one, and the goddess of speech
Carries: Speech, taste and the assimilation of subtle air
Related centre: Throat chakra
Related practice: Khechari mudra and the palate
Group: One of the eleven secondary nadis
Sources: Shiva Samhita, Gheranda Samhita, later commentaries

Where it runs

Saraswati is placed alongside sushumna and reaches the tongue, which makes it the channel most directly involved in the palate practices. Where lalana chakra is the target, saraswati is the route.

It is one of the few secondary nadis with a clear practical role, which is probably why it survives in lists that drop others.

The name

Saraswati is a river in the Rig Veda, later lost, and a goddess of speech, learning and music. The word means the flowing one. Both senses fit a channel: something that runs, and something that governs what is said.

The Vedic layer of naming is strongest in this part of the list. Saraswati, Varuni and Pusha all borrow a deity's job.

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Its centre