No, unless... the predators limit their own population in order to match the natural death rate of the prey. As soon as there are more predators than there are naturally dead prey, that means either a predator is going hungry or a prey is going to be hunted.

How likely is it that the predator is going to go hungry? How likely is it that the predator society will "rebalance" their numbers by eliminating one of their own? Some would say not bloody likely at all.

Let's factor in environment and go to the logical extreme. Let's say the ecosystem is at max capacity for prey, i.e.,  the prey are at max possible population for that ecosystem. The predator population can grow to consumer the number of naturally dying prey. Then add one more predator.