Even if its hooked up to the cage. On a stock seat it will basically flow over the seat and not have any guidance as opposed to a racing seat where it has specific holes to go into. Of course when things are ok it will hold the passenger snug, but in the case of a crash, the shoulder belts will come loose and depending on the impact, can cut into your passenger's neck. And being a fake harness could even break under load. A lot of people who decide to run seats and harnesses unfortunately do not take into account what would happen in a crash; which is when you need these things the most. They tend to go based on how they are like under normal driving conditions. Yes the fake harness on the stock seat will hold the passenger snug but thats only under normal driving. I definitely will never run a set up like that because it is way too risky.
From the few times I've been out on the track, I have seen so many people run harnesses in the wrong way. This guide should be of some help http://www.schrothracing.com/sdocs/2009_Competition_Instructions.pdf