"Do you have a staircase at home?"
Translation:Você tem uma escada em casa?
Yes, it would work. But you should note that there is a slight difference when you use "...na casa".
"Na" is the contracted form of "em" and "a" (em + a = na).
The "a" is the feminine article and it defines the noun. So, when you say "na casa", you are specifying that you know what house you are talking about.