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I really don't see any reason this would not work. You will need to make sure you have air circulation for the health of the tree and watering would need to be monitored.

Lovely garden!
Here are some links for you.

https://www.gardeningknowhow.com/edible/fruits/peach/peach-tree-care.htm
https://www.gardeningknowhow.com/edible/fruits/peach/peach-tree-thinning.htm

Here is an article that will tell you how to grow a peach tree from the pit:

https://www.gardeningknowhow.com/edible/fruits/peach/planting-peach-seeds.htm

Happy gardening!

From my research the seeds very well could also be diseased, depending on the issue with the parent plant.

I would advise purchasing new seed if propagating your own tree is the goal.

https://www.gardeningknowhow.com/edible/fruits/peach/planting-peach-seeds.htm
https://www.gardeningknowhow.com/edible/fruits/peach/peach-tree-care.htm

Here is an extension article (PDF) that explains why you are experiencing split fruit:

http://ext100.wsu.edu/benton-franklin/wp-content/uploads/sites/22/2013/12/Splitting-in-Peaches.pdf

Happy gardening!

August is generally not a good time for pruning, which should really be done once the tree goes dormant or in early spring. The best time of year to prune is in February, once the danger of frost has passed but before any fruit has begun budding/blooming. That said, it will not hurt to prune out what is dead and any weak branches, especially if they are crossing other branches.

Once the clean up pruning is done, if you have any fruit left on the tree this year, you need to thin it out. This article will help with that: https://www.gardeningknowhow.com/edible/fruits/peach/peach-tree-thinning.htm

It would be helpful to know what your climate zone is. If there is a peach orchard in your area, you might call the owner/manager and ask if the loss of leaves is normal for this time of year.