Using an Ideal 600 AAC Clamp Meter at the breaker box, do I measure both leads from the box and add them to learn the amps the motor is using? Each lead says 4.5 amps, so motor uses 9 amps? (The motor says 6.3 amps at 230 volts, but we have 240.)

4.5 Amps is your load at 240 volts. If each leg is NOT drawing the same, 1 side is leaking to ground or 120 volt devices and a neutral will be present.
With No neutral, both legs should draw the same.

Thank you for your answer. Much appreciated.

Your 6.3 A is likely FLA or Full Load Amps. Motors will draw a current depending on load.