Will this power inverter work with a solar system without batteries?

Probably no and probably not very well. Your solar panels are rated at a certain voltage (most panels like to run at about 18 to 24 volts). But they will change by the type of sun they get and the temperature outside. So since this power inverter requires an input voltage of 10 to 15 volts, your panels would have to be sending a consistent voltage in this range or the inverter won't work. Any voltage outside of this range will shut you down. Then your panels would also have to be able to keep up with the draw. My answer is that I doubt this would work unless you had just the right panels and just the right light and just the right load.