We just got one of the Chinese "new" treadle machines commissioned by Singer (number 15 reproduction), so I will be interested in seeing the answer. Why don't you try your treadle machine with thin leather and work up to thicker leather to see what it can and can't do? Some regular machines can do a lot more than you would expect.
You can disable the feed on those machines just by flipping a lever if you want to just push the material through by hand or move it sideways. I've seen videos of people using them to machine embroider by doing that. The lever also has positions for forward and reverse, like for reinforcing the end of a seam. I use the hand wheel for single-stitch advancement.