Q. Can a stained polished concrete floor be used in a house that does not have a cement floor?
A. If you are asking if a concrete floor can be installed in a house that has some other type of flooring, then polished and stained, the answer is yes.
After removing the old flooring you would need a minimum of 2" thickness for the new concrete floor. Concrete weighs 25 pounds per square foot @ 2" thick. Make sure your subfloor can hold the weight.
After the new concrete is installed you can stain and polish it for your new flooring.
Microtoppings can be applied over ceramic tile flooring. This is an ultra-thin type of topping that can be stained and polished also.