I wonder about the energy payback time or in that case rather the CO2 payback time. The CO2 released through production of silicon is not negligable (in fact for every silicon atom a CO2 molecule is released regardless of the CO2 released during the energy production)
I found an article from 2010 saying that the CO2 breakeven for solar PV was at around the 3-year mark. That article mentioned 225 W panels, the state of the art today is 400W with presumably the same CO2 load to produce. So that would put the payback at more like 2 years. It would get worse again to account for the energy losses in the desalination, CO2 collection and conversion.