I assume this is in the plant-only tank, the one with the extra plants but no fish. A whitish cloudiness is most likely a bacterial bloom. Common in new tank setups. The bacteria that reproduce rapidly in the water thus making it hazy or cloudy are those that eat organics. There are a lot of organics in tap water, microscopic so you don't see it. When you add conditioner to dechlorinate, you open the door for the waste-control bacteria and they multiply.
Yessir. The leftover plants in their own tank.
And it is a white cloudiness.
In essence, is this tank cycling just by having the plants in it?
Should I save the water when I actually go to set it up and use it?
There shouldn't be any chlorine in it, but I did not test for it. I am on well water.