Well, it's hard to predict what will happen - unless you fill the rear end with metal chips, ceramic beads or steel ball bearings. That piece of hose may do noting or it may do something. Just keep an ear out!
Sort of related example, my 02 Durango had a funny whirring sound when making a tight turn, like driving in a parking lot, but was steady for a long time (meaning not getting worse), but after about 50 K miles I thought I'd have a look. I pulled the cover off and immediately see one of the half round tubes that act as a barrier between the limited slip clutches and iron carrier was broken in pieces and stuck to the magnet at the bottom of the case, which looked like a porcupine from all the metal shavings, and the other half round piece was also broken and loose but sticking out of the carrier and rubbing on the case generating all kinds of metal particles. As I later found out this is a common problem with the 9.25 rear end in the late model Dodge trucks.
Me thinks that whirring sound was coming from the LS clutch pack because it was asymmetrically loaded since the one half round was in effect missing from the clutches and only part of the other side was still in place, and with a 1500 mile road trip coming up, I too didn't have time to deal with it. So I got the hammer and punch and proceeded to break the remaining hardened half round tube out of the carrier to at least put the clutch pack square or flat and cleaned off the magnet, put the cover back on and filled with oil. This was 100K miles ago.
