Does a good impedance match imply good balance and lack of common-mode currents?
Does a poor impedance match imply poor balance and excessive common-mode currenst?
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The two are separate figures, so one does not imply the other. A good match doesn't imply no common mode currents, and no common-mode current does not imply a good match.
They are somewhat connected - a change to the common mode currents will probably change the impedance match. But the other way doesn't have to apply - imagine soldering a small capacitor across the feedpoint. No change to common-mode currents, but the impedance match changes.
So these are both important considerations in an antenna design, but they are addressed separately, and with different techniques. Common mode currents are tackled by keeping things symmetrical, the addition of a choke or balun, or changing the antenna shape entirely. Then impedance matching is done by trimming (both sides of the antenna) and addition of matching components.