I don't think there is any problem with performance, however it's not clear to me why you would want to encapsulate Objective-C objects within a C++ object.
One reason to keep C++ purely C++ is so it can interact with other C++ objects, which is no longer possible once you include Objective-C objects.
In order to allow a C++ object, with an embedded Objective-C object, to be used by another C++ class (where it needs to "see" the header file) I guess you'd have to use void *
or something.