Yes, a dicky but still functioning O2 sensor can still send signals to the ECU in the 0.01 to 0.99 volt range, not throw a CEL code and make the ECU adjust the mixture all over the place not representative of what the actual O2 content is in the exhaust gases.
Take yourself over to the "Autoshop101" site, and read the tech article on 02 (closed loop) sensors for the nitty gritty on how they work.
I can't comment on the stainless steel wiring, its news to me, but does not mean its not true. You should be able to buy a sensor the same length as your current one.
Cost can run from $50 new to over $300 OEM. Search eBay for 02 sensors and get an idea on price.
If your economy is that good right now your sensor is fine, don't touch it.
Rich running over long periods kills a sensor, some additives in gasket goo can kill a sensor. Dropping the engine on its sensor can kill it also.