That depends what you mean.
If the question is, “Did humans die before the fall?” the answer is obviously no. In Genesis 2:17, God tells Adam that if he eats of the fruit of the garden, that day he will surely die. Paul affirms this in Romans 5:12: “Therefore, just as through one man sin entered the world, and death through sin, and thus death spread to all men, because all sinned—”
So, any theory of the Genesis account that allows the death of man before the Fall contradicts scripture.
But notice what these texts do NOT say. Neither Genesis 2:17 nor Romans 5:12 speak of death as it applies to plants, animals, or other living organisms. Romans 5:12 defines the death that entered the world as the death that “spread to all men.” The death of Romans 5:12 is a death that applies to sinful men as a consequence of their sinful nature. Therefore it cannot be applied to the rest of creation, because the rest of creation isn’t sinful in the sense that it rebelled against God, nor does the rest of creation fall under the category of “all men”. Furthermore, God says to Adam in Genesis 2:17 – “In the day you eat of it, YOU shall surely die.” God never threatens Adam with the death of anything but himself and his descendants, and it might even be asked, “If Adam had never witnessed death, what would this warning mean to Adam?”
Finally, notice God’s pre-fall command to Adam: “You are free to eat from any tree in the garden.” This means Adam had permission to end the life-cycle of living organisms in order to nourish his body, and God said that it was good. So if “death” is defined as “ending the live cycle of any living organism” then the answer is yes – there was death before the fall. But if death is defined as the punishment for humanity due to our sinful nature, the answer is no – there was no death.
So what about animals? While the Bible doesn’t specifically say anything about animal death before the fall, it certainly leaves the possibility. It doesn’t seem logical to conclude that God would allow the “death” of vegetation, but not other non-human living organisms. It’s certainly possible – but it’s also not clear.
Let’s recap: Was there death before the Fall? No. Yes. Maybe so.