No.
There are a number of issues.
The adults are very good at finding eggs, and will eat them. Any fry that hatch will equally be savoured by the adults.
In water with higher salt content, (ions, not "salt"), the males sperm has a reduced possibility of fertilising the eggs. This is in part due to the problem with the egg shells.
The eggs will not hatch. Any eggs that escape adult predation and become fertile are unlikely to hatch in regular tapwater. Calcium, (lesser extent Magnesium), ions in the water react with the eggshell. Even if the eggs were originally viable, the fry will not be able to break through the egg cases.
In the tropics, the sun comes up and the sun goes down. It is more regular there then in the temperate latitudes. The "light" issue with eggs is, IMHO, inaccurate. Rather, I believe that the nature of closed systems encourages the production of harmful pathogens.