In short
Untreated abscesses can heal on their own, but it's almost always a long, messy and painful process. Usually they heal without complications, but in bad cases they may lead to death, for various reasons.
The healing
Abscesses are encapsulations of foreign objects or bacteria and pusspus. This encapsulation prevents the inflammation from infecting surrounding tissue, but it also keeps immune cells from fighting the bacteria. (Source: Wikipedia)
The natural way an abscess heals is by breaking open and draining the pusspus out of the body. A doctor (or vet in this case) would do the same thing, but with a sterilized scalpel in a clean environment.
If the inflammation is well contained and doesn't effectaffect the animal too much, the abscess may stay intact for a long time, possibly till the natural end of life.
The risks
If this lump is actually an abscess, it's filled with pusspus and probably inflamed. This means physical stress on the body because the immune system is constantly active and fighting the inflammation, often resulting in fever.
In most cases the swelling is painful and very sensitive to touch. If the abscess is located near the mouth, it can hurt while eating or drinking, causing malnourishment in the animal. This further weakens the body.
Another consequence may be hair loss around the area, because the pain and itching induces scratching the skinskin. This is usually how the abscess is opened and drained in a natural way. Be aware that excessive scratching is a sure sign of pain and discomfort in a cat.
Depending on what caused the abscess and which bacterial infect it, the inflammation can spread and cause more abscesses in the same area or, even worse, can reach the blood stream and cause a sepsis (blood poisoning).
In bad cases, extensive regional tissue death (gangrene) may occur.
If the abscess breaks open and the wound is untreated, consequent contamination may lead to further infections.