Yes, and it would need to be a good potato, too, not an old, soft and shrinking one. Keep the leaf area of each cutting to a minimum. No more than a couple square inches. If you enclose the jar and all in a clear plastic bag to hold humidity in, it will be better (but no direct sun). If you do this, breath air in the bag just before you close it. The bag will instantly be holding more humidity than the ambient air.
Regarding the potato outside, it when it freezes it will turn to mush. I'm not sure how a cutting would react to that, but I don't think it would be positive.
