Freezing leftovers, will the potatoes turn to mush?

Agree with Nancy, the potatoes will not be inedible, they will just have changed in texture, to a more mealy consistency. I make a Brunswick Stew that similar to your Chicken Stew and always freeze at least half for later meals. I notice the texture change, but no one eating the frozen stew has ever mentioned anything to me. Why don't you experiment to see what you think?

Toni - you're right to worry that the potatoes (as any boiled or in a stew) won't defrost well. Instead, there are options.
Or: Just omit the potatoes from the stew, freeze, and eat without them once defrosted.
Or: Omit the potatoes from the stew when cooked & frozen, then boil some and add when you defrost and warm it up.
Or: Omit the potatoes from the stew when cooked & frozen, give with separate packages of another frozen starch (flour dumpling, matzo ball, polenta in squares or sticks, bread for putting under the grill) for use when you defrost the stew. Maybe even blocks of mashed potatoes, which freeze better than boiled ones.
Good luck.