The leaves or peat add tannins and some humic acids to the water. This usually causes the pH to drop a bit and slightly softens the water. It can't remove minerals that are already there, it simply adds some a acidic compounds. It can't make a huge difference to the basic make up of the water.
Trying to lower the pH of hard alkaline water can be next to impossible. The hard water minerals, the carbonates, have a buffering effect that strongly resists change, and you may end up having your pH bounce up and down, which is very stressful for fish.
If you need to change the water parameters, best to change the source water. The usual is to put in an RO filter and then remineralize the RO water to suit the fish species you want to raise or keep. Much more reliable, much safer, than trying to make hard alkaline water be soft acidic water.
If you have soft acidic source water, changing it to be hard and alkaline is fairly simple.. as it is with RO water. But the other way around rarely works very well. Of course it does depend just how hard and alkaline your tap water is to begin with.
Since my local water is very hard and alkaline, I chose at the start not to keep fish that must have soft or acidic conditions. I can't put in an RO system, it's an apartment.. and I was not able to lug expensive jugs of water home from the store either.