You can get a pretty nasty hum if the strings are not grounded. On steel covered strings a lot of the hum will go away once you touch the strings, which means your body is acting as the ground.
I didn't know that the originals came with tape wounds, but I would think that would be an even better reason to ground the tailpiece. The string core is still ferrous. I have a set of D'Addario tape wounds on an ES bass with a tailpiece. The "ball" on the bass end is colored metal which is conductive. The metal string core wraps around the ball, so a grounded tailpiece will ground the string, even if tape wound. The wrap is also pretty loose on the G string, so I am pretty sure it would ground at the bridge as well.
As to sound, YMMV, but I would not count on them sounding like an upright. I had a set of Fender tape-wounds that sounded a LOT like a fresh set of round wounds on my Frankenbass. You could play slap with them. The D'Addarios are far less lively, but still don't sound that much like an upright to my ear. Flat wounds sound more like an upright to me...and it's what my old upright actually had ;-)
BTW if you do get tapewounds, I'd stay away from the Fenders. Only bass string I have had in years that broke on me. I don't think I got more than a few months out of them.