Well,
Soap is a surfactant and will promote flow and break the surface tension of the liquid. A little soap probably won't do any harm. Baby shampoo or dish detergent. It'll make the solution easier to apply, it'll soak in better and faster.
PVA forms a skin by cross-linking of the molecules. Basically it's an aqueous acrylic emulsion, Acrylic molecules in water. Water based house paints are the same. If you let one dry right out it'll form an acrylic slab in the bottom of the can, effectively a lump of coloured Plexiglass.
After you paint on the PVA solution on the leather, the water will evaporate. When it's all gone the acrylic molecules 'join hands' (crosslink) and a plastic film is formed.
I can't see how adding oil will help.
If it intereferes with the crosslinking process a film may not form and the solution may not dry properly.
Watered down PVA on it's own with very little soap, just a drop, should do it. It'll be strong and flexible and water proof. It'll adhere strongly to the flesh side of leather, no problem.
Cheers,
Karl
*edited to correct the apparent inability of the author to write in his first language......