I think it is definitely possible..yes. I'll say that it comes down to pacing. An example could be getting the player to anticipate something for a while in order to scare them, leading up to something, through visual storytelling, a sense of unknown in area's of the level, sounds, feel of controls...
Then allow that anticipation to dissipate from the Player's mind. Have the Player see an item to go pick up easily, or do a navigation that is simple but requires attention. Maybe try a repetition in the level's design which causes the Player to lull into a feeling of safety and auto-pilot, cater to the player's expectations so their guard comes down...
And as the Player has just picked up the item and is about to continue on...as the Player has just landed on the platform and is about to make the easy jump to the next, the Player has let their guard down, and you reveal in full whatever it was that had been raising their anticipating earlier, the Player freaks out
Now all that anticipation and tension is burned off, so you will have to restart the cycle, you may even need some sections with release of tension in mind after the scary parts happen.
Limbo is a good example of atmosphere in two dimensions...obviously.
Another indie game I played which was tense and scary in some ways is Xeno Arena, it is top down 2d with a fog of war, and the enemies move very fast out of the shadows...
*edit*
I'll add that it isn't about making the Player think that they are there, that's not going to happen, don't assume 3d can also. It is more about playing with their expectations of what will happen on-screen when they interact with the controller. Another thought is that 2d games have the immediate advantage of the sense of unknown created by a scrolling view, there is less to show, and when you're trying to nail a certain atmosphere, it always helps to only have to show the things necessary (to do so)... also working in 2d with a plane of space allows usage of fundamental design concepts that can effectively lead the Player's eye and ultimately their thought process as they take in information.