Would an incarcerated ventral hernia always be accompanied by intense pain?

No--depends on...: ...What is "stuck" within the hernia. The most common tissue "incarcerated" is fat from just beneath the muscles; this is often painless. If it is internal fat from the omentum, this can be painful. If it is a loop of intestine, this causes a bowel obstruction or even compromise of the blood supply to the intestine ("strangulated" hernia)--this is usually very painful.

Not always.: If it is a chronically incarcerated hernia, it is often painless. But it can progress to strangulation without much warning. Consult a surgeon for specific advice.