Side-folding rifle stocks have been popular for decades. The chief benefit they bring to a rifle or carbine is a smaller, more easily transported package. Once an effective means of securing a carbine to the side of a paratrooper's body for jump operations, we find other uses for folders these days. Whether backcountry hiking, packing an emergency vehicle kit, or "riding fence" on your land, the folder's shorter overall length makes long arms compact enough to tote nearly anywhere. Most non-combat uses will allow shooters to deploy buttstocks prior to placing the rifle into operation, and for good reason. In spite of Hollywood and video game depictions of accurate hip shooting with nothing more than a pistol grip, engaging threat targets in this manner is inaccurate and undesirable.
I carried a number of rifles with side-folding or completely collapsible (non-AR style) stocks while in the military. The reason almost always had more to do with the method of getting into harm's way than how the rifle would be carried once there. One exception was during mountainous operations. My sniper buddies and I found that much of the movement through the jagged ridges of northern Afghanistan often required technical climbing skills—minus the pitons, chocks and ropes that make it somewhat safe. Free-climbing in extreme terrain is bad enough, removing daylight while adding a heavy rucksack, rifle and the possibility of being shot takes it to a whole new level of fun. The ability to remain hands-free and unencumbered was critical for maintaining contact with terra firma, while the ability to quickly place a rifle into immediate action was of nearly the same importance.
My experience is that the best way to engage a target with a pistol-gripped, folding-stocked rifle is with an IR laser and night-vision goggles. I found that I could be very accurate firing from an unshouldered position this way out to approximately 100 meters. Unfortunately, this technique only worked at night. As civilians, we're unable to own the same IR lasers our military and LE folks employ. If you're likely to find yourself in a position where your rifle's stock will be folded at a time when you need to fire quickly in the dark, you'll have to figure out another way to crack this nut. A visible laser is viable in this application, so long as lighting conditions allow ease of target acquisition. In bright sunlight conditions, even the brightest visible lasers are of limited use. A struggle to find the aiming point at the wrong time might be fatal. Since even visible lasers may be zeroed, you'll have to decide whether you want your point of impact to be parallel bore-sighted or set to coincide with the point of aim at a set distance. Both techniques have merits and faults.
Shooting your rifle from anything other than a solidly stocked shoulder position is a sketchy proposition. The best support can be gained by placing the firing hand against the body, near the hip. Avoid placing any portion of a heavy-recoiling gun directly against the body. Less accuracy is preferable to rolling around on the ground with a heavily bruised or fractured hip. Another trouble area can come from reciprocating charging handles. Since the rifle's action is typically placed close to the body when firing, it's easy to impede the charging handle's movement and cause a malfunction. With practice, you can make reasonable torso hits on man-sized target at ranges out to about 25 yards using hand-eye coordination only. I wouldn't plan for this style of instinctive shooting as a primary means of engaging anything. It's a contingency and nothing more.
Be sure your rifle's fire controls are usable with the stock folded. Many older designs partially or completely obscure the trigger guard, safety/selector, or both. Some bolt-action rifles block the bolt knob from operation when folded. The bottom line here is that just as with any other non-standard shooting technique, firing a rifle with the stock folded requires that you become intimately familiar with the firearm and thoroughly practice on a range with suitably high backstops before heading out the door.