Yes, a solar generator will work at night, as long as you have enough energy stored in your battery system.
Technically speaking, solar generators will not actively work at night because there is no energy from the sun to capture and transform into usable energy. Because the panels do not work at night, the solar generator is simply running from photons collected during daylight hours.
However, it is entirely possible to run a generator still, providing electricity at all hours of the day including at night.
Typically, solar power systems, including solar generators, will use one or both of two strategies for collecting and storing energy for use when the sun is not shining and the power grid is not available. The first strategy is to have a battery that can connect directly to the grid, charging and storing usable energy for later use. Check out Is a Solar Generator the Same Thing as a Solar Battery?
The second approach is, of course, to use the integral solar battery housed within the solar generator to store the energy gathered from the solar panels for later use. During the day, photons emitted from the sun hit the solar panel, are transformed into DC electricity, and that is stored in a solar battery. Depending on the size and style of the battery, it may be possible to use the stored energy for up to a week, at all hours of the day.
Please see “How Long Can a Solar Generator Run?” for related information.