It's 100% feasible to play a DA that's not in the know.
Just food for thought, but none of the Forbidden Lores the Dark Angels get have to do with the Fallen. The Forbidden Lores emphasis their secretive nature and their dealings within (and without) of the imperium. What do you do when you don't trust someone? you find out their secrets, you find reasons NOT to like them (and are sometimes surprised to find nothing to dislike heh). Rites of Battle specifically throws in Forbidden Lore: The Fallen. The DA use circles within circles for secrets, and your induction into knowledge of the Chapter is slow and steady. The first inclination that there are any renegade dark angels (at all) is when you hit the Ravenwing, when you get into the Deathwing, you know that the fallen exist, you know they're traitorous dark angels. The details are divvied up within those ranks, until you hit Supreme Grand Master who knows alllll the secrets, the whole story. That leaves (aside from members of the Deathwing assigned as Sgts to squads in other companies) all DA Tech-marines (aside from the Master of the Forge), and about 800 marines who don't know about the Fallen, and probably have no idea that there can even BE a renegade Dark Angel (unlike other more... liberal... chapters).
All of that being said, if you want Non-Fallen Oriented DA story goods, check out Purging of Kadilus Harbor (Nazdreg & Gazkhul vs DA 3rd Company w/Belial before he was 1st company captain). It doesn't get anymore non-fallen oriented dark angel than that aside from in the Deathwing Anthology that has the story of Two-Heads-Talking and the origin of the Deathwing's white armor vs Genestealers (though that anthology has a good story about a Fallen & a badass fallen dreadnought that I would love to model heh). You could also technically read the two Dark Angels Horus Heresy books, and Aaron D-B's shortstory in the upcoming HH Anthology for a look at Dark Angel mentality.
As to the blatantly obvious Fallen Blackshield, one of the reasons to play it is because it IS obvious, it's so obvious, if your PCs don't play here and are that flavor of skeptical, no one will think of it, kind of like hiding in plain sight heh.