Yes, the old deities are really coming back. Along with the list of old deities in the Forgotten Realms section of the gods listed in the updated basic rules, (and the gods listed amongst many pantheons in the Player's Handbook) there is also the "Sundering" story line. The Player's Handbook lists 39 deities for the Forgotten Realms setting with their domains and symbols. And 24 "non-human deities" which are shared between Greyhawk and Forgotten Realms.
During the Sundering the worlds of Toril and Abeir (which were united during the Era of Upheaval) are being separated from each other. During this time, the various gods are creating "chosen" mortals who are intended to bring power to the gods, in the hope that when "things are settled" these gods will have the power required to remain a god. There seems to be confusion amongst the gods as to what Ao actually has in mind as he re-writes things.
Noted events during the Sundering are the diminishing of Spellplague effects, magic changing its nature to the way it worked in the past, such that old spellbooks work and recent ones do not. "The Weave" has new prominence, and most importantly for this question, various gods are found to either not be dead, to be re-united, or to be recreated through various events. It seems that in the various divine schemes to "get enough followers" all divine who have a "chosen", get chosen to remain a god, in a fun twist of the meaning of the "chosen".
Short answer: Yes
Christian and Christian-themed elements, in the very early years of Dragon Magazine, did in fact get some coverage. An article called The Politics of Hell in Dragon 28 (warning that it "cannot be considered the official doctrine of" AD&D) presented a history of Hell's struggle against God as played out on an interpretation of modern Earth, and included stats for "Astaroth," "Belial," and even "Satan" himself, an absolute beast of an adversary with such features as a move speed of "whatever is necessary" and an immunity to attacks made without "purity of heart."
The traditional Christian orders of angels - seraphim, thrones, powers etc. - appeared in Dragon 35. They were preceded by generic angels of healing and wrath, the archangel of mercy and a prior seraphim in Dragon 17. These began to be displaced by more familiar (and less religiously-inspired) celestials in Dragon 63 and 64, a displacement that has never been rolled back.
Let us not forget the clerics
Explicitly noted in prior editions for similarities to the Knights Templar and Hospitalers, clerical orders were noted in the 2E PHB to be "frequently found on the outer edges of the Christian world."
Several cleric spells both old and perennial are derived from or show strong ties to the Christian mythos - Elijah's miraculous calling of fire from the heavens, for instance, suggests flame strike; create food and water recalls the loaves and fish, water walk, tongues, sticks to snakes, insect plague... there was at one time in the core PHB a spell literally called part water and I doubt I need to suggest the origins of that one.
And of course there are the other names...
While Satan was off the table for full canon status, likely due to the expected taboo in their major market, other names from Christian sources did make it through. Lucifer was the other major casualty - Ed Greenwood has suggested that this was another name for Beherit, a fallen archdevil. Dragonlance poked around at the borders with the gods Paladine (named E'li by the elves) and Habakkuk (a Biblical prophet), the retributive deity St. Cuthbert still bears the unusual honorific and was suggested to have traveled from Earth, and the names of various fiends derive from Biblical pagan gods and idols - Adramelech, Moloch, Belial, Baalzebul, Dagon - to say nothing of the innumerable fiendish names derived from Christian demonology.
What about God?
Ah, now there's the great taboo. After the great moral panic, it took a long time for TSR to nudge back onto that ground. When they were feeling bolder, they included some minor notes on Christianity at the end of an article regarding gods of the Dark Ages - Eostre, Mannus, Woden - and gave the following parameters: "lawful neutral or lawful good clerics with the bonus proficiency of Read/Write Latin."
Dungeon 86 included an adventure, "Mysterious Ways," set during the Crusades and explicitly invoking messiahs, the "True Cross," and other Christian trappings. It still doesn't mention God or Jesus by name, however. There may be other adventures in a similar setting in official publications; I know of none offhand, however.
To make a long story short: Taboo
By and large, anything the average layperson would identify as core Christianity has been kept to the margins, left implied, or almost entirely untouched over the course of the game's existence. If it would suggest that Yahweh is on a similar footing as Zeus, Odin or Ra, it's been left out.
Best Answer
In the new 5e module Tomb of Annihilation, the Grung goddess Nangnang is prominently mentioned. However, few details are given (it almost seems intentionally so). So, the 5e Forgotten Realms Grung have at least one specific deity, if not more.
(SPOILERS FOR TOMB OF ANNIHILATION BELOW)