Chain plates are positioned parallel to the hull's exterior, placed fore and aft of the mast to work in unison with the standing rigging. Bulkheads are perpendicular and not necessarily where the chain plates are located. The amount of movement will be dictated by the design and the integrity of the build, but there will be movement ...minimal if your boat's design places the upper stay chain plates on the bulkhead, as noted above.
I had first-hand knowledge of this by not being able to fully close a passage-way door that was framed into a bulkhead ...until the the rig was completely eased; then the door latched just fine. Finally had to plane the door (1/4" +/-) so it would close with the rig tuned. That's an extreme case, but there's a lot of force involved and movement.