Not flaming you Dr.Sound, but that is not true in my experience. I ran without the MIL eliminator hooked up for weeks, and the only down side was the CEL (MIL) came on.
The second O2 sensor is used to compare the outputs pre and post cat to make sure that emission system is working. Now, if you run without the second O2 sensor installed, you may go in to limp mode. I had mine installed, just not with a MIL eliminator.
I'm going on 6k miles with mine installed (soldered per instructions) and have had no problems at all.