It doesn't matter what the panels doing at night or any other time of day. All that matters is the net power usage (amount generated - amount used). During peak times, he'll likely be feeding power back into the grid which will help pay for A/C during non-peak times.

Batteries don't matter at all...the grid is your "battery". You basically "store" the excess electricity you generate in the grid until you need it** Obviously, the disadvantage is that if the grid goes down during a period when you're not producing peak power, you're done (unless you just use a standard UPS).

Adding batteries to a grid-tie system is a great idea, but it adds a lot more cost and maintenance. Maintenance is almost non-existent on a battery-less system. The more batteries you add, the more difficult they are to maintain, because the batteries have to work together. If one is not operating as well as the rest, it can reduce the efficiency of the whole bank. This can make a tremendous difference in how well your system performs.

**This may vary from country to country and even by utility company. In the US, the utilities buy back the power at retail, vs. wholesale, so you get exactly 1kwh back for each kwh you generate.