I would think a lot of them probably do, melody-wise, but I'm unaware of any one where that specific claim is made. I know that some sources (e.g., Dr. Ragheb Moftah, if I recall correctly) say that the tune of "Golgotha" is taken from ancient Egyptian pre-Christian funerary chant, but I don't think that's actually substantiated anywhere musicologically/archeologically (see below); it's just a view that is popular among Coptic people. Coptic music is a bit of a contested topic in terms of its origins.
The
Coptic Encyclopedia entry on Coptic music states:
Scholars do not agree concerning the antiquity and purity of the Coptic musical tradition. Admittedly, without notated manuscripts, it is virtually impossible to unravel the sources of the many melodies. Nevertheless, specialists who have studied, transcribed, and analyzed this music concur that, at the very least, it does reflect an extremely ancient practice. Ernest Newlandsmith (see Musicologists, below) traced it to pharaonic Egypt, whereas Rene Menard, a bit more cautious, proposed that those melodies sung in Coptic descended from the pre-Islamic era. In all probability, various sections of the music, like the numerous texts, were introduced into the rites during different stages of the early Coptic church, and the music as a whole does not date from any single era or region. It is clear, however, that the musical tradition has continued unbroken from its beginnings to the present day. Hickmann considered it a living link between the past and the present.
And
Despite Greek influences in the urban centers, in the pharaonic temples and throughout the rural areas in general, ancient Egyptian music continued to be performed. “The people thought, felt, and sang “Egyptian’” (Hickmann, 1961, p. 17). Horudsha, a harpist, and ‘Ankh-hep, a temple musician and cymbal player (both first century A.D.), are two professionals whose
names indicate their Egyptian roots.
Hickmann proposed a connection between the Kyrie and the ancient Egyptian rites of the sun-god, and according to Baumstark, a litanic form of the Isis prayer is found in the Oxyrhynchus Papyrus 1380; even the invocations of the saints in the Roman formulary are closely related to this ancient cult. In the Songs of Isis and Nephthys (Middle Kingdom texts, trans. both Faulkner and Schott), evidence exists of antiphonal singing, which still remains today as a basic feature of Coptic music (see ANTIPHON and Description of the Corpus and Present Musical Practice, above). This practice was also known among the Therapeutae, an ascetic sect of Alexandria (c. 100 B.C.). Another Coptic musical characteristic that might have existed in pharaonic Egypt is the vocalise and/or melisma (see Description of the Corpus, above). After research into Middle Kingdom texts, Hickmann suggested that certain repeated syllables (transliterated by him as xe, xe, xe. . . , khe, khe, khe, . . . ) might be interpreted as such. Further, some Gnostic texts contain vocalises said to be built on the seven “magic vowels.” Pseudo-Demetrius of Phaleron referred to this phenomenon as well, calling it “kalophony.” Other holdovers from ancient Egypt could be the use of professional blind singers in the performance of the liturgical services (see Cantors, below), and the use of percussion instruments in certain rituals (See Musical Instruments, below). Hickmann and Borsai felt that the folk songs of Egyptian villagers have melodies and rhythms similar to those of Coptic chant. Much more research needs to be done, however.
