Eric,
If your alternator size is adequate there is no reason for it not to service the stereo & stereo batteries until the desintation is reached and the engine is turned off. This might extend your playtime, reduce discharge levels and prolong the batteries lifespan. After depletion you would not re-introduce the alternator, in any case, to the stereo battery bank again within the context of that day. So on that basis the alternator/stator capacity is good info to have.
Planning on having a substantial shore charger?
Did you plan on using the above mentioned Gen on the boat as standard equipment? If so, will the charger be asked to function as a power supply/convertor?
What kind of play time at rest are you expecting?
Will the volume be kept at a level that is safe for children and will it be louder on occasion with adults only?

David