Yes, a metro goes somewhere. That said, the only 'metro' (personally) I ever talk about in English is the one in Paris. In London it's known as the Underground (Londoners like myself call it the tube) and that is what I tend to call all underground systems, except when in the US: I say 'subway' when I'm there.
The question would rarely be asked, unless the trains that use the same tracks can possibly have different destinations -- which is entirely possible in some systems. I can easily imagine someone at the Rockefeller Center subway station here in New York asking "does this train go to Queens?" and being told "no, this is the B train; it goes to the Bronx."