Can a solar inverter be damaged if installed capacity is much larger than demand?
An inverter can indeed supply a lower current than the solar panel rating without any system damage to the system. 

If an inverter is not supplying as much power as the panels can deliver it will simply draw less current from the solar panel. If you follow the IV-curve of the solar panel you will see that lower current from the panel allows the voltage to increase toward the panels open circuit voltage.
The solar panel is not damaged by sypplying no current, and providing the inverter can withstand the maximum ("open circuit") voltage the panels produce it will not be damaged.


Image taken from this question

The solar panel output voltage varies both with load current an temperature. The colder the panels, the higher is the output voltage. But in a good design the panels should be chosen and connected to the inverter in a way that they can never exceed the maximum voltage rating of the inverter.