the short answer is no. Grid down, so is solar generation, typically. Most invertors are the "cheap" types that require a working grid so the invertor works. There are invertors that work "off-grid" but these are only used in solar powered facilities that have no grid connection.
A UPS is different as these tend to be isolated from the grid. ie the grid provides the charging for the batteries and the batteries discharge through an invertor that doesn't connect to the grid (directly).
So the longer answer is you need the more expensive invertors that work independently of the grid. But you then have an issue with whether it is a "hot" handover on mains fail or a "cold" handover where you lose power and then have to manually start the invertors. Either way you still then have power, for a little while. Long term better off with a diesal or hydro system.
