So, does this theory check out?
Like most fan theories, believing that Eleven is the monster on Stranger Things requires interpreting many symbolic, thematic, and metaphoric elements of the story as literally as possible. It takes a show filled with mysteries and ambiguities, and demands all those aspects conform to a "twist" that's never fully explained in the text itself. Obviously, Eleven and the monster are linked -- even the most basic reading of the show would acknowledge that -- but are they really the same?
That will be the most interesting part of this theory going forward, whenever Netflix inevitably announces a second season. Judging from what we see in the show, Eleven genuinely cares for Mike and his friends. Only in episode five, when she directs the compass away from the laboratory, does she deliberately attempt to sabotage their efforts to find their friend and uncover the mysteries of the Upside Down. If she's secretly a villain, she's doing a bad job.
Also, it's clear from the final episode that this isn't a Tyler Durden-style situation. As viewers, we see them share the frame together, and other characters watch them do battle as well. Instead, a looser interpretation of this theory could suggest that Eleven is the monster yet somehow exists independently, as if the monster were the flip-side version of Eleven.
And while a stoner's post-bong-hit observation in support of this corollary might go, "Dude, the number 11 reads the same right side up and upside down -- whoa!" one thing connecting Eleven and the monster is a certainty: the monster and Eleven probably both enjoy Eggos. Because, seriously, what kind of monster doesn't love a good Eggo?