An interface in C++ can be defined with the help of an abstract class. So, if the question is if you can have a constant member variable you can. However, a constant member variable cannot be changed during program execution. You can do this with the help of a configurable flag provided in the interface.
I will strongly advice against the above for 2 reasons:
1) Interfaces should normally have member functions. An interface is a collection of abstract methods. The main functionality of an interface is to serve as a bridge between the user and the inner functionality. This interface should more or less remain constant throughout the product lifecycle. Therefore, having a constant bool does not make sense from an OOP standpoint.
2) If you want to initialise an object, a constructor is the best way of making sure that it happens. Therefore, initialisation then depends on object instantiation in your product and you will not need to write support functions to do so.