A General Quarters drill starting between 0730 and 0745 on Sunday morning won't result in their day being "filled with work." It consists of sounding General Quarters and manning battle stations as if you were going into combat. If there's not been any sign of an attack by, say, 0815, you can then just secure from General Quarters and return to normal operations. It means half an hour to an hour out of the day being spent, not actually working, but being ready to jump into action if something happens. It might be a rude awakening, but it's hardly preventing the crews from having their day off.
Besides, there is, or at least was (I don't know if it's still true) a longstanding tradition in all navies of manning battle stations (sounding general quarters, sounding action stations, beating to quarters, whatever term you want to use for it) just before dawn whenever at sea--because before the advent of radar, sunrise was the earliest time one could get a good view of what's around you, meaning that if an enemy has closed in on you overnight, come the dawn, they could sneak-attack you before you can react. Thus, you put everyone at their battle stations and get ready for a fight just before dawn, so that you won't be taken by surprise. If there's nobody there, then you can just stand down, but if there is, you've mitigated the damage. Having a dawn General Quarters drill on Sundays in Pearl would be an extension of that; if you feel that it actually needs to be justified, you can always share the "war warning" message with your officers and chiefs (who would be able to keep a lid on it, but also assure the enlisted men that yes, there is a reason for this, and no, you're not cleared to hear it).