No - the shield needs to be connected to the point of lowest electrical potential, which may or may not be at the source. The point of lowest electrical potential is the mains earth and the point where the signal return connects to it (along with the metalwork of the case). This will not be at the source if the source is double insulated and uses a two core mains lead.
If the cable has its shield connected to earth at the preamplifier, then regardless of whether the other end is connected to a source or not, the pick-up of noise will be minimal.