Firstly, I believe the space junk has a net angular momentum around the Earth's rotation axis. That is because it is launched with angular momentum from the Earth's surface and usually in the direction of spin.
Second, the individual bits of space junk are capable of inelastic collisions that result in kinetic energy, but not angular momentum, being lost.
If these things are true then eventually the system will settle into some configuration with minimum kinetic energy for a given angular momentum, which will be a disc-like structure. However, most space junk is in low-Earth orbit already. If it loses kinetic energy then it will re-enter the Earth's atmosphere and burn up.
I wouldn't know what timescales this might happen on - collisions between bits of junk are reasonably rare - but one danger is a few big collisions might trigger a collisional cascade; much the same process (among planetesimals) is thought to produce debris disks of dust around some stars.
As @rob points out, if the timescales for inelastic collisions are too long, then interaction with Earth's extended atmosphere will drag the space junk down before it can form a disc.