Some vaishnavas use the classification of puranas into sattva, rajas and tamas. Do Gaudiya vaishnavas accept classification of puranas based on three gunas?
Yes, Gaudiya Vaishnavas accept the guna-based classification of the Puranas. This is what Jiva Goswami states in his "Sri Tattva Sandarba":
yad uktam matsye: pancangam ca puranam syad akhyanam itarat smrtam sattvikesu ca kalpesu mahatmyam adhikam hareh rajasesu ca mahatmyam adhikam brahmano viduh tadvad agnes ca mahatmyam tamasesu sivasya ca sankirnesu sarasvatyah pitrnam ca nigadyate
As the Matsya Purana [53.65, 68 — 69] states, "A historical text is a Purana if it has the five defining characteristics; otherwise it is known as an akhyana. In Puranas describing days of Brahma in the mode of goodness, the Supreme Lord Hari is mostly glorified. In those describing days in the mode of passion, there is especially glorification of Brahma. In those describing days in the mode of ignorance, there is glorification of Agni and of Siva. In those describing mixed days Sarasvati and the Pitas are discussed. (Sri Tattva Sandarba 17.3)
atragnes tat-tad-agnau pratipadyasya tat-tad-yaj -nasyety arthah sivasya ceti ca karacchivayas ca. sankirnesu sattva raj as tamo mayesu kalpesu bahusu. sarasvatya nana vany-atmaka-tad-upalaksitaya nana-devataya ity arthah pitrnam karmana pitr lokah iti srutes tat-prapaka karmanam ity arthah.
Here glorification "of Agni [the fire-god]" means of Vedic sacrifices which are executed with offerings into various sacred fires. In the phrase "and of Siva also," the word "also" implies "also of Siva [his wife]." "During mixed days" means during the many days of Brahma in which goodness, passion and ignorance are all prominent. "Of Sarasvati" means of various gods who are indirectly indicated by reference to her, since she is the presiding deity of various kinds of verbal expression. "Of the Pitas [celestial forefathers]" means of the ritual activities which lead to attaining them, in accordance with the sruti statement, "By Vedic rituals one achieves the world of the Pitas." (Sri Tattva Sandarba 17.4)
tad evam sati tat-tat-kalpa -katha-mayatvenaiva matsya eva prasiddhanam tat-tat-purananam vyavasthajnapita taratamyam tu katham syad yenetara-nirnayah kriyeta. sattvadi-taratamyenaiveti cet sattvat sanjayatejnanam iti sattvamyad brahma-darsanam iti ca nyayat sattvikam eva puranadikam paramartha jnanaya prabalam ity ayatam.
Such being the facts, we can understand that the Puranas mentioned in the Matsya Purana are divided into natural categories according the kinds of days of Brahma they contain narrations of. But how can we define a hierarchy of these categories to determine which is superior? It might be suggested that this can be done with a hierarchy of the modes of nature — goodness, passion and ignorance. If so, we can conclude that Puranas and other scriptures in the mode of goodness have the most authority to teach us about transcendental reality, according to the reasoning of such statements as "From the mode of goodness knowledge develops" EBg. 14.17] and "In the mode of goodness one can realize the Absolute Truth" [Bhag 1..2.24]. (Sri Tattva Sandarba 18.1)