If your signal is "transparent" enough go through so much rock and iron without being absorbed (like neutrinos), you'll have a hard time capturing it on the receiver side.
Well, OPERA was 700ish km, but had Cern at one end. If one has this as the sole goal and wanted to do it real-time over 12,000km is it "engineering-possible" vs "theoretically-possible" ? My guess is that it depends how much money stands to be made ;)
https://en.wikipedia.org/wiki/OPERA_experiment