When you say mashed potatoes, do you mean real leftover mashed potatoes dressed with milk and butter or olive oil in or just plain “naked” mashed...

I don't know about this specific recipe, but I have a potato bread recipe that I have made many different ways with different potatoes and it always turns out just fine. Generally, there isn't enough milk or butter or what-have-it in the potatoes to affect the recipe that much. I've used baked potatoes, steamed potatoes, boiled potatoes and mashed (seasoned and all with butter and the works) and my bread turned out fine, any way I did it. So I suspect, you can use whatever you have on hand as long as you measure it out.