Obviously this is a stunt. Stunts are important in the development of new technologies, because they're a way of pushing the limits of the possible in a quasi-sporting mode (i.e., to hell with the expense), and getting publicity.
Fossil fuels will be necessary for aviation for the foreseeable; therefore all the more need to replace fossil fuels wherever possible elsewhere, so that total greenhouse emissions can go down while still keeping air transport possible (I do know greenies who are opposed to aviation, and motor cars, and growth: but they're really puritans, and there are plenty of others who are actually just concerned about the environment). Solar Explorer may have some impact here, just as car racing has some impact on the vehicles we drive.
So yes, this has got bugger all to do with practical aviation directly; but it might have some indirect benefit.