Can pixels on the image plane be mapped to world space coordinates?
What you are asking about is 'mouse picking'. If a user clicks a pixel on the screen how can you get corresponding world space coordinates of an object being clicked on. 
Imagine a ray from that pixel, through the view volume all the way to the far plane. That ray is a set of all possible points the user is clicking on. So we want to perform ray/poly ntersections with every object in the scene, and return the first intersect.

To transform the pixel into world space, you first have to turn your x,y point in screen space into NDC coordinates (-1 to 1) use -1 for your Z component and 1 for W to create a 4 float component vector and then multiply that vector by the inverse projection and then inverse view matrices.
There are many examples of this process if you want to see code, but this is the basic process. 
Now we have a ray from the camera/eye position into the scene, we want to do intersection tests with our objects. There are many ways of achieving this, take your pick.

Hope this helps, good luck!