Would a renewable grid provide power in the night, or when wind is slow?

Sure.  At a point when we're approaching a grid 100% powered by wind and sun, we'd also be approaching 100% use of electric vehicles.
 
EV owners are already using something called  demand-side-management: their cars can charge when power is cheap.  This doesn't cost the grid anything at all.

If the 230M vehicles in the US had 50kWh of storage each (more than a Leaf, but less than a Tesla), that would be 11.5 TwHrs of storage, all provided by vehicle owners. That's about 24 hours of grid output. There's enormous potential for absorbing diurnal variance in wind & solar (and nuclear) output, with large savings to drivers: they have to charge sometime, so the large variation in prices during the day would be more than enough to cause owners to program their cars to automatically arbitrage between different times of the day.

It may be hard to imagine an all-electric fleet with that much storage, but that's where Tesla's planning to go.