Random question about Desperado....how does he have any emotions whatsoever, or even the capability to feel? His Essence is .01, literally the most cybered-out you can get without becoming a Cyberzombie.
The way I look at it is that you don't have deadened emotions until you actually reach zero, and at that point you need -really- expensive (as in out of the reach of PCs) equipment to keep you alive. Memory inducers have to periodically kick in and remind you that you're still alive, coupled with powerful magic that keeps your soul from escaping your body. Those unfortunate folks are called Cyberzombies. Trust me. You don't want to be one.
At such a low essence though (low but still above zero), your soul is stretched thin, on the precipice. But it's still intact, albeit barely. As Josi said, he's probably closer to having some sociopathic tendencies at times, but like the main character in Gross Point Blank, he still has a personality. He's still animated. He still enjoys things.
What will affect you though is how well magical healing works on you. At lower essence you can still be healed magically, but it's really difficult for the mage trying to mend your wounds. At 6 essence, healing spells are as normal. They require Willful x1 to not get drained. At 3 to 5.99 essence, that goes up to Willful x2 and at .01 to 2.99, Willful x3 is needed. Without that level of Willful, healing those with lower levels of essence can cause headaches, fatigue, nosebleeds and the like. All in all, it can be fun to RP out the mage saying "Geez, chummer! Are you chromed up enough?! I think you might be able to squeeze a little bit more into your body there."...