But on this one,the short answer is, No.
If Dark Matter were to have manifested in 2D, it would not interact with gravity. The whole reason Dark Matter was hypothesized in the first place was because of a noticeable gravitational effect.
If Dark Matter was 2D until it interacted with normalized matter, as you put it, then we would not see that gravitational effect previously mentioned except in bits and pockets and our galaxy would fly apart at the seams.
There are a lot more problems with '2D matter,' but this gets the idea across...