There will be a limit, of course, and it is quite complicated. I don't know exactly how the associated circuitry is configured, but there will be a minimum voltage across the cap below which it the circuitry won't supply current (and the battery will start to be used). There will continue to be some drain beyond that point through the cap's internal resistance (which tends to be proportional to its capacitance, all other things being equal) and the circuitry's "off" resistance. The voltage across a cap is calculated by dividing the charge in it by its capacitance [edited to correct the original error flagged by dalecoy], but the current output from a solar cell (at constant illumination) is relatively constant within a working range of voltages, and some of that charging current will be wasted bringing the cap back to its minimum operating voltage. The bottom line is likely to be that some increase in capacitance will be beneficial but a huge (e.g. tenfold) increase is more likely to be self-defeating.
