(note: screenshots were missing from old wiki, links removed from here)
As you can see, it does work, yes this is Transgaming's WineX doing this, not normal Wine.
I have actually had more success running TTD on Linux in Regular Wine - in WineX the Sound effects don't work properly. But, I thought I'd post this as evidence that it can and has been done.
This was using WineX 2 and 3 (tried both, exactly the same result) and TTDPatch Alpha 25