They do accept The link with Madhva Sampradaya and Gaudiya Sampradaya. First of all Srila Baladev Vidyabhushan was not the direct disciple of Lord Caitanya, he was the disciple of Visjwanath Chakravarti Thakur (An Acharya in the lineage of Lord Caitanya). Srila Baladev Vidyabhushan accepts Gaudiya Sampradaya as a lineage of Madhva Sampradaya and gives the Parampara list as follows
With great devotion we glorify the spiritual masters in the Gaudiya Vaisnava disciplic successions. A list of their names follows: 1) Krsna, the Supreme Personality of Godhead, 2) Brahma, 3) Narada, 4) Vyasa, 5) Madhvacarya, 6) Padmanabha, 7) Nrhari, 8) Madhava, 9) Aksobhya, 10) Jayatirtha, ll) Jnanasindhu, 12) Dayanidhi, 13) Vidyanidhi, l4) Rajendra, 15) Jayadharma, 16) Purusottama, 17) Brahmanya, 18) Vyasatirtha, 19) Laksmipati, 20) Madhavendra Puri, and 21) Isvara Puri, Advaita Prabhu and Nityananda Prabhu (who were all disciples of Madhavendra Puri). We worship Isvara Puri's disciple, Lord Caitanya Mahaprabhu, the Supreme Personality of Godhead, who delivered the entire universe by granting the gift of krsna-prema (pure love of Krsna). (Prameya Ratnavali, Text 7)
Kavi karnapur was However the direct Shiksha Disciple, even the name Kavi karnapur was given to him by Lord Caitanya Mahaprabhu. Kavi karnapur also accepts Gaudiya Sampradaya as a lineage of Madhva Sampradaya and gives the following Parampara list
paravyomesvarasyasic chishyo brahma jagat-patiù /
tasya sishyo narado’bhut vyasas tasyapa sishyatam //
suko vyasasya sishyatvaà prapto jïanavabodhanat /
vyasal labdha-krishna-diksho madhvacaryo mahayasaù //
tasya sishyo’bhavat padmanabhacaryo mahasayaù /
tasya sishyo naraharis tacchishyo madhava-dvijaù //
akshobhyas tasya sishyo’bhut tac-chishyo jayatirthakaù /
tasya sishyo jïana-sindhus tasya sishyo mahanidhiù //
vidyanidhis tasya sishyo rajendras tasya sevakaù /
jayadharma munis tasya sishyo yad-gana-madhyataù //
srimad-vishnu-puri yas tu bhaktiratnavali-kritiù /
jayadharmasya sishyo’bhud brahmanyaù purushottamaù //
vyasatirthas tasya sishyo yas cakre vishnu-saàhitam /
sriman lakshmipatis tasya sishyo bhaktirasasrayaù //
tasya sishyo madhavendro yad-dharmo’yaà pravartitaù /
tasya sishyo’bhavat sriman isvarakhya-puri-yatiù //
kalayamasa sringaraà yaù sringara-phalatmakaù /
advaitaà kalayamasa dasya-sakhye phale ubhe /
isvarakhya-purià gaura urarikritya gaurave /
jagad aplavayamasa prakritaprakritatmakam //
Brahma, the master of this universe, was the disciple of the lord of the spiritual
world. His disciple was Narada and Vyasa became the disciple of Narada. Suka
became Vyasa’s disciple through the awakening of spiritual knowledge.
Madhvacharya took initiation in the Krishna mantra from Vyasa. Madhva’s disciple
was Padmanabhacharya, whose disciple was Narahari, who was followed by
Madhava Dvija. Madhava’s disciple was Akshobhya, who was followed by Jayatirtha,
Jïanasindhu, Mahanidhi, Vidyanidhi and Rajendra. Jayadharma Muni was one of
Rajendra’s many disciples and Vishnu Puri, the author of Bhakti-ratnavali and
Purushottama the lover of Brahmin culture became his disciples. Vyasa Tirtha, the
author of Vishnu-saàhita, was Purushottama’s disciple. Lakshmipati Tirtha, a
reservoir of devotion, was Vyasa Tirtha’s disciple.
Madhavendra Puri was the disciple of Lakshmipati, and it is by him that this religion
was founded. His disciple, the sannyasi Isvara Puri, took up the mood of conjugal
devotion, while Advaita Acharya [also the disciple of Madhavendra] took up the
moods of servitude and friendship. Gaura (Caitanya Mahaprabhu) accepted Isvara Puri as his guru, and then
flooded the material and spiritual worlds [with divine love].
There was a Saint of the name Hariram Vyas, he was the disciple of Madhavendra Puri (Gurus guru of Lord Caitanya Mahaprabhu mentioned in all biographies of Lord Caitanya) and he later took up the Radha Vallabh Sampradaya and he gives the following list
sri-krishno bhagavan brahma narado badarayanaù |
sri-madhvaù padmanabhas ca nriharir madhavas ca saù ||
akshobhyo jayatirthas ca jïanasindhur dayanidhiù |
vidyanidhis ca rajendro jayadharma-munis tataù ||
purushottamo brahmanyo vyasatirthas ca tasya hi |
tato lakshmipatis tataù sriman madhavendra-yatisvaraù ||
isvaras tasya madhavo radha-krishna-priyo’bhavat |
tasyahaà karuna-patraà hari-ramabhidho’bhavam ||
Read the names here it is in Sequence.
Coming to Jiva Goswami he does accept connection and addresses them as his Predecessor in his Tatva Sandarbha
And says that he is accepting whatever Madhvacharya Quoted without even seeing the Shlokas in the original Scripture and accepts the wordings the Acharyas in his line.
Even in the Pushtimarg Vallabhacharya lineage, his grandson accepted that Madhavendra Puri was a Madhva Tatvavadi Vaishnav and gave Sanyas to Vallabhacharya.
Narhari Chakravarti Thakur in the lineage of Srivas Acharya and the son of the disciple of Vishwanath Chakravarti Thakur he in his Bhakti Ratnakar mentions the Story of Diksha of Nithyananda Prabhu in the Madhva Sampradaya by Sripad laxmipati Teerth the disciple of the famous Madhva Sampradaya Acharya Vyas Teerth.
Accept the words of Acharyas. Infact Even the Madhva Sampradaya Acharyas like Srila Vishwesha Teerth Swami Maharaj and other great Acharyas accept that Gaudiya Sampradaya is a lineage of Madhva Sampradaya and Lord Caitanya took Diksha from the Madhva Sampradaya. The proof is the Udupi Ashtha Matha Letters to Gaudiya by the Madhva Sampradaya Acharyas
This is the link. If u are unable to open this link then just search Udupi Ashtha Matha Letters in Google and u will find it.
All glories to Guru and Gauranga, All glories to Srila Prabhupad, All glories to Vaishnavas