Is it still a tourist landmark if the landmark isn't there? Yes!
A friend of mine is living in Copenhagen. From a recent report on his blog:
This morning, we had an excellent, traditional Danish breakfast consisting of bread and things to put on bread. It's such a good culinary concept. Then, G drove me and E2 into Copenhagen. We saw where the famous Little Mermaid statue is usually. Unfortunately , it's on loan to China for the time being. In its place was a large television screen displaying a still photo of the statue. Hilarious.
This is a totally unoriginal thought, but here goes: we don't go to tourist landmarks because they are inherently interesting per se. We go because everyone else has gone. We go because the it occupies some greater status in culture and history--it's not a statue or a building but a Landmark, a gathering place, a site that is, like a celebrity, famous for being famous.
In this case, though, I think the television screen is probably more interesting than the statue it's temporarily replacing (if you're easily amused by irony and disappointment, that is). After all, to take a photo of the real deal is to capture what is probably the least-flattering of all not-so-flattering photos: