No. The theory you describe is not accurate.
Lightning Protection does not cause nor can prevent a structure from being struck by lightning.
All earth-based objects emit streamers when the air is electrified from an approaching storm. When the charge separation occurring within a cloud reaches a critical point, a stepped leader(s) is emitted from the cloud towards the earth. If you, a tree, or your building just happens to be the earth based object in which the connection is made, the stroke occurs.
If your building happens to have a LPS, the stroke attachment is more likely to occur at the strike termination device which has an intentional low impedance path to earth. If your building does not have a LPS, the stroke attachment may occur anywhere on the structure and cause destructive currents to flow over high-resistance paths. In either case, neither building is any more likely or any less likely to be struck.