My answer to this question is "no".
The Anapanasati Sutta is about the Four Foundations of Mindfulness. It says:
Mindfulness with breathing, developed and cultivated, fulfils the four
foundations of mindfulness.
In the Anapanasati Sutta, each of the last 14 of 16 stages is preceded by the phrase: "a bhikkhu trains thus" or "he trains himself" (in Pali: "sikkhati").
In other words, while the Anapanasati Sutta using four tetrads describes fulfillment of the four foundations of mindfulness, the fact the Anapanasati Sutta uses the term "he trains himself" shows it is not the practise of Arahants because Arahants are no longer engaged in "training" ("sikkha").
This fact is shown in the suttas where the Buddha's own practise of Anapanasati is described, such as in SN 54.11, where the phase: "he trains himself" is not found.
In addition, each stage of Anapanasati is experienced with knowing of breathing. However, knowing of breathing is never mentioned in both the suttas and commentaries by highly esteemed monks as an experience in jhana. In jhana, there is no knowing of breathing, which shows, per Commentary teachings of three types of samadhi, there are different degrees of experiencing rapture.
Thus, while this distinction is not mentioned in respect to the Buddha's meditation in SN 54.11, in SN 54.11 the term anāpānassatisamādhiṃ (concentration due to mindfulness with breathing) is found. In other words, a Buddha or Arahant may start their meditation with Anapanasati but the concentration developed from it will quickly proceed to jhana.
In summary, what distinguishes stream winner, once returner, non returner & arahant appears to be the attainment and use of jhana. The suttas, such as Iti 96 & MN 14, say: (i) a non-returner never returns to sensuality; and (ii) a practitioner that has perfected jhana is no longer tempted by sensuality. Therefore, it appears what results in non-returning is the perfection of jhana.
Bhikkhu Bodhi has made a clear case (i completely agree with) that a stream-enterer has not yet reached jhana. Refer to: The Jhānas and the Lay Disciple According to the Pāli Suttas.
In conclusion, it appears the progression through the four stages of awakening (stream winner, once returner, non returner, arahant ) is related to whether jhana or not is leading the insight (vipassana) of the four foundations of mindfulness.