Is Out of the Abyss D&D + Call of Cthulhu?

The flippant answer is that, of course, it depends on the GM and the players.  But, more than just about any other product that I'm aware of, it can be, and it's deliberately set up so that it should be.  In many ways.

It should be noted that anything with demons in it has been slowly approaching the CoC paradigm for many years now.  From the very beginning, demon lords like Juiblex were clearly influenced by notions like the shoggoth, although I suspect that the immediate inspiration for most demon lords (that aren't from the Judaean or Christian traditions) have more to do with the Elric Lords of Chaos stuff than anything else.  But there are notable similarities between the Lords of Chaos and the Yog-Sothothery tradition.

An early cameo was the mention of Dagon in the 1e Monster Manual II.  Dagon is, of course, an actual Philistine or Canaanite figure, but Dagon in D&D was always a wink and nod to Dagon of Lovecraft's The Shadow Over Innsmouth.  Finally, rather late in 3.5's life-cycle, we get him statted up and formally described, and he's exactly like the Lovecraftian version.  Also, this book finally gives us the obyriths—demons as described more by Lovecraft than by Christian traditions, complete with a form of madness ability that causes minor insanity.  Less clinical and complicated than the venerable CoC Sanity system, but clearly meant to employ the same vibe.

Now, in Out of the Abyss, we formally get all of the demon lords treated that way.  I don't even know if there's still the formal split between obyriths and tanar'ri or not (I lost track of most of what was official in D&D at the end of the 3.5 era) but if the Abyss (and its inhabitants) are supposed to be the domain of madness—chaos and evil—then why wouldn't they?  As I explained many years ago already now, it seems like Cthulhu himself is best seen as a demon lord, if he were put into D&D terms, and the notion of the Far Realm always did overlap with that of the Abyss anyway.  They are conceptually exactly the same thing, but aesthetically they haven't quite always been on the same page, because the Abyss has lots of Judeo-Christian demonology folklore involved in addition to its overt Lovecraftiana, whereas the Far Realm was "pure" Yog-Sothothery.

Then again, Lovecraft himself used Dagon, didn't he?  And ghouls.  He wasn't against using "traditional" horror elements if he thought he could get them to work.  So, in every sense, the dichotomy is a false one; but it seems I'm hardly the only person to have noticed that.  The designers, in an attempt to prune a cosmology run amok, have followed that same pattern in many respects.  Demons that are like shoggoths, demons that cause madness, and in general, a lessening of references and mentions of the Far Realm altogether.  I doubt it'll go away completely in D&D, because nothing ever does as long as it has some fans somewhere.  But it also doesn't need to be heavily promoted when there's really no reason for it to exist.

So, how does Out of the Abyss compare to CoC other than the notion that the demon lords are acting more like Lovecraftian Old Ones?  Let me quote some sections of this review for it briefly (I've corrected a few minor typos in brackets:

[T]his is the best look at the Underdark since Night Below – another amazingly well done campaign in a completely alien environment. In Out of the Abyss, the Underdark is creepy, weird, and danger lurks in the darkness…which is nearly everywhere since you’re underground. The foreword of the book says that Lewis Carroll’s writing was an inspiration for this slight reimagining of the Underdark but the end result feels more like something Robert Chambers would [write] – familiar and yet not at all right to our sensibilities. In fact, Out of the Abyss deserves an even closer comparison to the game Chambers is best associated with –Call of Cthulhu. 

Like Call of Cthulhu, Out of the Abyss tests the sanity of its PCs due to their encounters with strange and horrific beings beyond our usual comprehension. Why shouldn’t Demogorgon have the same effect as Hastur or Shub-Niggurath on a PC? I love that the Out of the Abyss team took this approach. Now the madness checks in Out of the Abyss are not the same as the ones you would have encountered in 2e/3e Ravenloft. It’s a much more simplified process, but it also allows for stacking mental disorders, which is always fun. It is very easy to turn Out of the Abyss into a horror campaign rather than your normal fantasy D&D campaign and I dare say you are doing yourself (and your players) a disservice if you DON’T run it as one. 

And here's some more:

For gamers who have braved things like The Tomb of Horrors, Beyond the Mountains of Madness or adventures with that 1970s/80s flair of “your character is probably going to die horribly at some point,” Out of the Abyss will no doubt trigger some fine feelings of nostalgia for you. That isn’t to say that Out of the Abyss is geared only towards gamers who caress their copies of OSRIC lovingly, but that those gamers will probably get the most out of this campaign because they know what to expect. This not only makes Out of the Abyss a great way to get older gamers who have, until now, steadfastily refused to try anything D&D without the TSR stamp on it to finally give 5e a try, but it’s combination of 1e aesthetics, Second Edition’s use of horror and alien imagery and 5es easily understandable ruleset makes this a fantastic choice to bridge the generation gap between the different D&D fans in your family and/or friend group.

It's curious that he tracks Tomb of Horrors and Beyond the Mountains of Madness as having the same "flair" which I disagree with.  The only thing both have in common is that it's likely many PCs will die playing it.

Appendix D is “Demons” and here is a little taste of what a 5E Fiend Folio [would be like.] [...] Here you’ll find tips on how to play the [monster] as well as the action they can (and will) take when in their base of operations. The second is “Regional Effects” and how the[y] warp reality in their local vicinity. Now by local I mean between one and ten MILES depending on the demon. Hey, you’re dealing with otherworldly creatures that have between three and five HUNDRED hit points and an AC of at least 18 (but usually 20 or over). These things are powerful, even if you are a level 15 Mage. This section is really well done and even if you don’t ever play on playing, it might be worth picking up just to see how the demons are designed. So spoilers of sorts – here are the eight demons in the book: Baphomet, Demogorgon, Fraz-Urb’luu, Graz’zt, Jubilex, Orcus, Yeenoghu, and Zuggtmoy. They’re all fun and the art is fantastic. I won’t be surprised is some people find a few of these to be more than a little similar to some Mythos or Warhammer deities though.

To be fair, I think this is part of the reason why I like this adventure/campaign so much, but I also admit that I like the format much better than, say, the overly detailed Adventure Path paradigm.