So your battery will act as a ‘time-shifter’ for charging your hot water storage? And only if, there wasn’t enough PV during the day.
If hot water demand is your largest electric use then this focus seems to make sense.
However, I still think a diverter will in practice help out. Maybe on intermediate intensity solar power days you might be able to heat the tank up totally on solar (without battery boost), but you will need to follow the PV system output in order to get your got water tank full. Without a diverter you might end up exporting where you still have a cold tank.
But it depends on price of that diverter…(always easy to add a diverter later aswell)