You'd still have the time the sun is not shining, which would likely be more expensive than before (a gas powered plant would only be running half the time - effectively doubling its capital/construction cost per kWh).
So you'd definitely have an improvement on some levels but I'm not sure that would really help that much.
The real big breakthrough would be somme big improvement on storage. I'm not convinced this will happen quickly (at least not in anyway similar to the declining cost of PV panels). The consumer electronics industry has been paying $$$ for decades for better batteries/battery r&d and has seen pretty poor gains.
I think Tesla and the electric car manufacturers will definitely rapidly get the price down by say 30% because of economies of scale but will then hit a brick wall as more of the cost becomes raw materials, transport, etc which will set a floor on the cost of batteries.
Happy to be proved wrong though :)