I don't think the new alternator will make any difference.
The rating of an alternator (in this case 720 Watts) is how much power it can potentially supply, if (a) the power is actually demanded by the bike and (b) if the alternator is turning fast enough.
The issue here is not that the alternator on the 1200 is under specified. Even if the alternator was rated at a million Watts, if the engine is not turning fast enough, it wil not be able to supply that much power. If the engine speed is sufficient, the standard 600W alternator is more than capable of charging the battery and running all the electrics on the bike with plenty of power left over for auxiliary lighting and all the other gizmos GS riders love to fit.