If I'm using bare leather I like to keep it bare, it doesn't have to be soft and supple... I'd be concerned that the oils in skin products would work to lubricate the surface and remove any real benefit to stropping on bare leather in the first place. There are silicates in the skin that are responsible for the polishing action, so you want the blade making full contact with it. Now if you are using a compound then it really doesn't matter, but I wouldn't do that to any strops I intended to keep bare.
I could be wrong with my thinking, but it is just that... it's my