A few things
1) Warp travel, as has been previously mentioned, is possible without Navigators. It's just sucks.
2) The Astronomican is already invisible in the Eastern fringe around Ultramar. They use other psychic beacons for navigation.
3) Navigators can still Navigate without a beacon, they just don't have the continious reference point which makes things easier and safer.
And as for the Emperor dying
1) There's the whole "Acension to true godhood" thing that may or may not happen.
2) The Emperor is sitting on top of a giant warp gate from when Magnus's sorcery screwed up his attempt to seize control of the Eldar Webway. He's only left Terra once since that, and that was to fight Horus. Malacor the Sigilite, a supremely powerful psyker, took his place during that time and the strain of preventing the Earth from getting eaten killed him. So Terra is gone along with the HQ of the Inquisition and the Officio Assassinorum. The HQs of the Navy and the Adeptus Mechanicus are now very close to a very scary warp rift.
3) Space Marine Librarians can communicate astropathically without being soul bonded. There are other ways of being soul bonded that don't involve the Emperor, although they might be unsuitable for Astropaths.
4) It's really likely the Imperium will start fracturing (it'll take a while though, the feudal and widely spread nature of the Imperium means it'll take a while for the effects to be felt).