As I came to a conclusion that a direct binding between single checkbox and Boolean property of underlying managed bean would not be possible I tried to create my own converter. Although it works for the edit field e.g. if I put '0' in the field the managed bean property is set to false, if '1' is used then the respective property is set to true, it does not work with checkbox field.
From my testing it seems that getAsObject method of the assigned converter is never called (but getAsString is called properly).