Are Quick Peanut Butter & Chocolate Squares Sturdy for Mailing?

I would not ship the peanut butter and chocolate squares, for exactly the reason you suggest - that the temperatures while en route in the mail could - very likely would - melt the chocolate topping.

Also, I doubt the topping could be covered tightly enough to keep the bars fresh without smushing the topping down, detracting considerably from its appearance. ;o)