Did the pumped hydro dams they built alongside nuclear power plants replace the baseload? No, they took the cheap energy that was produced at times when it wasn't needed and provided it back at peak times. They literally increased the base load by propping it up when it would otherwise droop at night (mostly).

It charges, when electricity prices are low, which generally means off peak overnight.

In a future renewable grid, with zero dispatchable power it might be used on occaision to help meet the baseload, but it's almost certainly going to be used more during demand peaks, because that's when most electricity is used. Maybe in equatorial regions with a lot of solar, not much wind and no other energy sources it'll share baseload duties with the solar that charges it during the day, but unless the term baseload has lost all meaning (which I fear it has) storage is not ever providing baseload, since that would imply supplying that amount constantly and storage needs to absorb more energy than it returns.

I can't see a definition of 'baseload' provider that storage meets that solar doesn't for example.