Would a global cooling event disable solar energy usage?
I am not sure about the size of Krakatoa eruption but the eruption of Mt. Pinatubo in Indonesia around 12th June 1991 is considered as the largest eruption in the past 100 years. Global average of decrease in solar radiation after 4 months of eruption was about 2.7 +/- 1 W/m^2. Global average surface reaching solar radiation is about 198 W/m^2. In other words, Mt. Pinatubo eruption caused about 1.3% decrease. 

The number 2.7 W/m^2 is a global average, so the decrease might have been more in tropical regions and less at high latitudes. It took about three years for stratospheric aerosol amount to return to the background level. 

Reference: 


Minnis et al., 1993, "Radiative climate forcing by the Mt. Pinatubo eruption", Science, vol. 259, 1411-1415, doi: 10.1126/science.259.5100.1411 
Kremser et al., 2016, "Stratospheric aerosol - observations, processes and impact on climate, Review of Geophysics, vol. 54, 278-335, doi:10.1002/2015rg000511