Well when I think of 2.5d i think of isometric games like RTS, Rollercoaster Tycoon etc where it's faking 3D at an angled perspective. So you could for example make something like Theme Hospital where it shows depth, do you mean a game like this?
If you mean front-facing a platformer that contains 3D objects then you can use the z-elevation or your own effects as mentioned in that post above. I'm no artist but I'd say you could probably fake it with scaling of objects to give that effect.
To answer your question, yeah the player character would move, there is something called parallax where some layers scroll more slowly and can give that 3D effect. You could probably fake walking into a background by scaling the player and having a layer of objects in front of the player. I'm not an artist so I've not tried any of this but it might be possible to do what you want.