Mine was like that too (
http://s151.photobucket.com/albums/s138/arew264/Benz%20Climate%20Control%20Thermocouple/) . I managed to find the other half by some luck, but it snapped about the same way.
It is supposed to be glued into the grille piece, but I'm guessing that with age on ours the glue disintegrated/died/whatever.
Yes, that hose pulls air past it. It commonly disintegrates as well, so make sure all is well there.