Can a piece of metal with a specified shape resonate at a certain frequency?
Indeed, an unconnected piece of wire will have a self-resonant frequency

What you are describing is basically identical to an parasitic element on a Yagi-Uda (or just Yagi for short, or often "beam" for the pattern it puts out) antenna.  Whether it be a reflector (longer than half-wave) or director (shorter than half-wave), its pickup of the radiated wave from the driven element allows it to reradiate that EM wave, and the fact it is shorted at the middle creates a phase shift, causing the pattern to change.