Great question! It will NOT work, though!
Busy Lights hear sound through the cord that goes from their wiring box into the headset jack or the handset jack of the telephone. The speaker phone doesn’t route through either jack or use a cord. So there will be nothing for the busy light to pick up.
Sidenote: Why are we using speakerphone to begin with? Chat up the benefits of headsets and conference mode if your Customer ever asks about this!