"I've heard that some people use the knife with the blade facing them [demonstrates ice pick grip]. Is that practical?"
According to western novelist Louis L'Amour, who worked as a merchant mariner in the 1930s and saw combat in WWII and was also a pro boxer, this was the correct way to use a knife. He was also a mule skinner for a while, which might account for his gruesome appreciation for the knife.
Holding the single sharp edge of your knife toward you is not a sound dueling orientation for the edge. But dueling with knives is crazy. This is a murder grip, or, in military terms, a sentry removal grip, which I have documented the use of in The Logic of Steel.
The ice pick grip is also a sentry removal grip, not a functional dueling posture.
If one uses a reverse grip you are seeking to stab in and then rip out. You should rip cut in the direction you are moving, not standing there taking a bath in his entrails. I like having the edge facing out, as I can slash in a limited fashion incase the stab is jammed and most importantly because I want to move to his right, toward his weapon hand as I rip open his belly.
If you use a reverse grip with the blade inward then you are ripping down or to your right and his left—unless, and this is where the reverse grip with edge in comes into it's own—he is facing away from you and your are taking his back and cutting around his right arm and stabbing up into his lung above the liver. One could easily stab himself in the belly, balls or leg rip-cutting with an inward edge from the ice pick grip.
The other way to use a knife with edge-in is to carry it low around your hip in a standard grip and break in on your man with the checking hand—maybe with a coat or jacket in the off handstabbing him in the guts just above the pelvis and ripping upward into his cage. Ideally you just stab upward beneath the left rib cage and puncture the heart. The "military" method demonstrated by MacYoung in his classic knife fighting book is ideal for this.
This edge-in blade orientation permits no slashing, only stab and rip.
This discussion should shed some light on why double-edged knives [classified as dirks] are outlawed by many states and are preferred by many military and paramilitary operatives.
Fighting Smart: Boxing, Agonistics & Survival