Yes: they are different functions, they can have different exception specifications.
If a virtual member function has an exception specification, any override (not overload) must have an exception specification that is at least as strict as the member function being overridden.
Of course, you should "never write an exception specification" except in those few situations where you must.
Visual C++ does not fully support exception specifications, so it allows some code that is not actually valid per the C++ language specification. The warning you mention just means that you are using code that uses a C++ language feature not supported by Visual C++:
A function is declared using exception specification, which Visual C++ accepts but does not implement. Code with exception specifications that are ignored during compilation may need to be recompiled and linked to be reused in future versions supporting exception specifications.