On the level of game mechanics, the classic D&D cleric melds the healer, the crusader and the witch/vampire hunter in one person. Is this a genuine D&D mish-mash or is there any cultural/literary predecessor this very concept harkens back to?
The D&D Cleric, apart from its Blackmoor origins as a vampire hunter (as noted here), is a mish-mash that has grown into a trope of its own.
The D&D cleric as a trope, encompasses:
The Cleric was one of the three Original D&D† classes; the other two were Fighting Man and Magic-User.
The Cleric as evolved to add priest of specific cults - the original presentation almost ignored the deity.
In fact, the original published presentation is short enough to quote:
(D&D Original Edition, 6th printing, Vol 1, page 7.)
So, we have hybridization to some degree directly in evidence - The D&D cleric is aligned not to a deity, but an alignment. This is counter to almost all historical models, save those of the dualistic religions (Zorastrianism, especially). We have the Hammer Films anti-vampire hunter (Holy Symbol, Holy water, repels undead that others can't). We have the Medieval "Fighting Priest" of the Romances (ahistoric, but historically loved) coupled with the priest-friar tending to a fighting company as chaplain (historic, but best beloved because of the legends of Robin Hood containing Friar Tuck, who combines both). We have also priest as landowner - a nod to medieval abbots and bishops. The use of no edged weapons isn't explicitly given an origin that I've seen, but appears to be a "thematic" element arising from the early Christian Conciliar prohibition on clergy causing the shedding of blood, coupled to a lack of grasp that blunt weapons also are quite capable of drawing and shedding blood. (A grazing mace will in fact rip you open nicely if you aren't armored.)
More evidence of mashup are the titles for the levels:
(D&D Original Edition, 6th printing, Vol 1, page 16.)
Acolyte, Vicar, Curate, Bishop: All used in western churches, including Roman Catholic, Church of England, and Lutheran (tho' not all Lutheran Synods).
Patriarch is used in the Roman Church for 4 particular Archbishops; its use is far more common in the Eastern Churches - The Eastern Rites of the Catholic Church and the Orthodox Churches. Orthodoxy also uses Acolyte, Priest, and Bishop.
Adept and Lama are borrowed from elsewhere - Adept from a variety of pagan traditions, and Lama from the Tibetan... for Abbot. Which is itself an interesting placement - Abbots rank below bishops in Orthodoxy and Catholicism - but in the Early Irish church, were the ones appointing bishops.
Notably missing are the subdeacon, deacon, archdeacon, dean, and archbishop of the Catholic and Orthodox churches, and the High Priest common in pagan traditions, with the gaps filled by other traditions' titles. A sure sign of mish-mash.
Later editions, in addition to expanding the spell repertoire, add priests of specific mythoi, and priests of specific deities within a given mythos. They also provide alternate titles.
D&D has had an influence, however. Fighting priest-spellcasters have become an accepted trope in fantasy fiction, even tho' the majority of priests in the Sword and Sorcery genere were one of three facets: Bookworm preacher, spellcasting priest, or warrior monk; all three can be found in the Conan stories. The D&D cleric has migrated into the video games and into a few Manga and Anime series. It has infected later RPG's, as well - the Shugenja of L5R has more in common with D&D clerics than with Shinto or Buddhist monks.
† Ignoring supplements for the moment.