Yes, the people and media should work correctly through GEDCOM. The GEDCOM file just contains the file path to each referenced file on your system, so as long as you're on the same computer, no problem.
I meant to write earlier that I agree with your comment about the layout of FTM. It's very intuitive: people, places, media, sources, publish, and search. It could perhaps use another tab in there for facts/events, but overall it's a very nice way of dividing up the different ways of looking at your data. In fact, it's a rather common sense way, but as someone who uses another genealogy program, I can tell you that FTM's layout is way better. Common sense ain't that common, I guess.