Does the saṅ­kha­ta­lak­kha­ṇa of dukkha apply to the noble path?

from description of Sariputta's attainments given by the Buddha himself, Ven Sariputta used Sati as vehicle to enter (tho entering is not quite correct term to use, but for clarification purpose only) cessation from neither perception nor non-perception. At cessation, sati ceases to exist (sati is part of name-form-and 7th of noble paths), therefore, sati is Dukkha. at cessation or Saññā Vedayita Nirodha all 8 noble paths cease , as does name-form. noble paths are pratityasamutpana dhamma. ven. sariputta continued to enter cessation in and out several times, to see the rise and fall of name-form. wisdom or vimutti-yanatasana does not occure while one is in neither perception nor non perception or cessation state.

In MN 24, "The Relay Chariots" sutta, the Supramundane Path is the last stage of the Seven Stages of Purification. While being the highest, it's still 1 of the 7 "Relay chariots" used to reach the final destination which Nibbana the unconditioned. Since it's not the destination itself, it's still conditioned dhamma.

I found an explicit statement in the Visuddhimagga (XVI.566):

[...] atthi cettha dukkhaṃ na ariyasaccaṃ, [...] tattha maggasampayuttā dhammā sāmaññaphalāni ca “yadaniccaṃ taṃ dukkhan”ti (saṃ. ni. 3.15) vacanato saṅkhāradukkhatāya dukkhaṃ, na ariyasaccaṃ[...]

(transl. Bhante Ñāṇamoli:)

... (a) there is suffering that is not noble truth... "89. Herein, (a) though states associated with the path and the fruits of asceticism are suffering since they are suffering due to to formations (see § 35) because of the words, "What is impermanent is painful" (S II 53; III 22), still they are not the noble truth [of suffering]..."

thanks for your help!

All the best.

Theravada recognizes only nibbāna as unconditioned -- thus, not dukkha.

Other schools have disagreed on what is unconditioned:

In the Sarvāstivādin tradition since the compilation of the Dharmaskhanda, three unconditioned dharmas have been recognized: analytical cessation (pratisankhayā-nirodha), nonanalytical cessation (apratisankhayā-nirodha) and space (ākāśa). In the Theravada tradition, only one unconditioned dharma, nirvana, is recognized (Dhammasanghani p.244), a position also maintained in the Agamas and by the Vātsīputrīya school. According to the Samaya, the Mahāsanghika, Ekavyavahārika, Lokottaravādin, and Kaukutica schools all recognized the following nine unconditioned dharmas: (1) analytical cessation (2) nonanalytical cessation (3) space (4) the realm of infinity of space (5) the realm of infinity of consciousness (6) the realm of nothingness (7) the realm of neither consciousness nor unconsciousness (8) the law of dependent origination (9) the law of the noble path [...]. The Mahīsāsaka school also recognized nine unconditioned dharmas; but its list differed somewhat from that of the Mahāsanghika school and included such items as immovability, the eternal law of good dharma, the eternal law of bad dharma, the eternal law of indeterminate dharma, the eternal law of the path, and the eternal law of Dependent Origination. The law of Dependent Origination was included in the list of unconditioned dharmas because it was regarded as an unchanging principle. The Sarvāstivādins disagreed with this position and did not recognize the existence of a principle of Dependend Origination separate from conditioned dharmas. For the Sarvāstivādins, the law of Dependend Origination itself was conditioned.

For the Mahaśiśākas, the path to nirvana was recognized as an unconditioned dharma because the practices established by the Buddha were considered to be eternal truths. The Sarvāstivādins opposed this position by maintaining that although nirvana was unconditioned, the wisdom the Buddha had realized was conditioned and not eternal.

-- A history of Indian Buddhism: From Sakyamuni to Early Mahayana