For sure, and that can definitely work. But, you will need three times the number of solar panels (since half the time the panels are doing nothing and if you're storing a lot of energy, that means there's a proportional amount of storage losses.)

And I honestly don't know how much mass in batteries would be needed for 15 days worth of storage, but my instincts say too much.

Keep in mind that total mass to deliver can sometimes be the biggest cost limitation. A nuclear generator that gets delivered in one launch could be cheaper than otherwise much simpler solar panels and batteries if that solution requires two or three launches.