The effect of overcapacity is null or negative price, which has the property to make more storage viable (who cares if it only gives back 25% if the input is free or very cheap), so I'd say intermittent sources overcapacity is an enabler of on grid storage.

E.g. today in Germany you can buy MWh at 14€ at 13:00 and sell it back at 180€ at 18:00. I didn't look all of Europe but it looked like the biggest spread today... You can make money with crappy storage under those conditions...