Can a solar system be connected to a grid without a battery storage system?

Yes, the grid acts like a battery for you. See it as the cheapest battery you can buy. It won’t go dead on you when you need it and it can give you all the power you want when you want it. The only downside is power failure. So it would be cheaper to own a generator for those rare occurance and use the grid to store you extra electricity. Batteries are expensive and don’t last forever and have to be replaced.