I run one of our trucks without a sway bar. We used it around the property mostly, with the occasional drive to town for supplies or fuel. I also plow with it. The ride really is better without the bar, BUT the truck is a handful at speeds above 55 when loaded... It would be VERY easy to over-correct, swap ends, and roll if you were a typical driver.
As Shovel pointed out, the MAIN purpose of the font sway bar is to ensure understeer in limit handling maneuvers. Without the front sway bar, you'll find that it takes very little steering input to snap the rear of the truck around on the highway, especially when loaded. Some people are better drivers than others, and may be able to control a truck with no sway bars in an emergency, but I'll suggest that most people are NOT in this category...
It also makes a difference if we're talking solid axle or IFS... IFS has a higher roll stiffness without the sway bar, making the bar a little less critical. Solid axle vehicles have a lower roll stiffness, and so the sway bars they use are generally stiffer.
If you mostly drive back roads, and always empty, I'd say you won't miss the bar, and likely you'll find a somewhat better ride in the rough. If you load the truck, or drive highways more, I'd say you NEED it if you don't want to end up as a fatality. Remember, you don't have to screw up, all you have to do without a sway bar is try to avoid someone else who screwed up. If the speed is greater than 55 or so, my bet would be on you whipping the tail and heading off the road sideways, which is not a good plan in a higher CG vehicle...
Good Luck!!