The net effect of this is that electricity originally generated by nuclear plants and other fossil fuel plants gets 'converted' into (more expensive!) 'green' energy.
It's a kind of white-washing for electrons. The price difference can be substantial more than making up for the cost of the pumping and subsequent re-generation.
And of course it's the energy sold to the public that matters, not how it was originally generated so by double counting this energy it changes the balance considerably without there actually being more renewable energy to begin with.
Currently both pumped and hydro are making up about 1% of the UK grid each: http://www.gridwatch.templar.co.uk
It's only useful to think about it in the short term as long term it adds nothing. It just functions as a buffer.
You can go round one in Wales: http://www.electricmountain.co.uk
This is not renewable energy though it masquerades as such. Note that before green energy became a thing this was already happening so it is simply a re-labeling rather than that these lakes suddenly got re-purposed for renewable energy storage.
If the source of the electricity is not originally renewable energy then it is deceptive to sell it as such. People pay a pretty premium for renewable energy.
Pumping upward typically happens when the renewables are overproducing and the (controllably) variable power plants are idling. It makes no sense to run the pumps for storage when you could throttle back the gas turbines instead. But you can't adjust cloud cover, or tweak windspeed. So when the sun is shining, and the wind blowing, and the methane not burning, you store that excess for later.
That may also include relatively constant baseline power plants. But even then, the storage is often allowing those plants to run at their optimally efficient design capacity. If you idle the coal plant to 80% rated output, you may still be using 85% as much coal (made-up numbers for illustrative purposes). Trying to adjust the output of a nuclear plant is rather complicated, and may involve altering shutdown and maintenance schedules such that the output capacity several months in the future is affected by a decision made today.
So on the whole, re-generation from pumped storage is going to be greener than the baseline plants, and definitely greener than other types of adjustable peak load power plants, like natural gas turbines.
A big part of US climate strategy seems to be to install a lot of wind and solar power and fill the rest with natural gas, phasing out coal. Keep the nukes that are there. That's possible since in the USA, natural gas is cheaper than in many other places.
As for the bookkeeping:
A certain amount of electricity is produced using renewables which is always < the current baseload. It is then (much) more profitable to sell this energy to consumers directly and then to use the reduced base load requirements to top off the lakes before reducing base load generation capacity. At night the process reverses and now the 'newly minted green electrons' get added to the green energy already being sold. This makes more money than selling the nuclear/coal/NG generated electricity directly even though there is some loss from the whole pumping operation.
Note that the scheme already made money based on the demand pricing of electricity, the 'green' aspect simply made it more profitable.
In some situations, even pumped storage storing non-renewable power power is "greener" than you seem to imply. The problem is that nuclear generators can't stop producing electricity when it's not needed; let's say you are France and a large part of your electricity is generated with nuclear power. If you can't store your energy, during the night you're producing power that you need to waste away. And during peak hours, you need to turn on many gas turbines to get additional power.
If instead you can store your additional energy during the night, and use that one during peak hours, you burn less fuel and pollute less.
This is one of the early large ones, built by the local utilities:
