Question: "If Adam and Eve hadn't sinned, introducing death into creation, wouldn't the world have gotten overpopulated?"
Answer: When God first created Adam and Eve, when they were still in the Garden of Eden, He charged them to be "fruitful and multiply, and fill the earth" (Genesis 1:28). When He cursed Eve in Genesis 3:16, He told her He would greatly multiply pain in childbirth. Both passages imply that it would have been possible for Adam and Eve to have children in Eden (although there is no indication they did). If death had not entered the world, and if all of Adam and Eve's descendants had followed God's admonishment, eventually, the world would have been filled. But would it have been overpopulated?
This is one of those questions that usually come from a deeply entrenched modern mindset. Fear of pollution and famine and unemployment permeates our world. Almost one third of our land mass is desert. It is very likely that, in our world, if fertility rates were untainted by sin, and if no one ever died, the world would indeed become overpopulated.
However, the question does not concern Adam and Eve in a fallen world but in a perfect, sinless world—a creation imbued both with eloquent natural law and God's miraculous power. Imagine an unfallen world with no desert, no wilderness, no unproductive land at all. Imagine a sinless creation producing many times more than our fallen world ever could. Imagine unfallen, sinless man wisely overseeing the earth’s resources and living in a charitable harmony with each other. Such a world would be completely foreign to us.
Eventually, however, the perfect, sinless world would have been filled. What then? To assume that an unfallen world could slide into something less than ideal is to doubt God's sovereignty and creative power. He told Adam and Eve to fill the earth, and He would have had a plan once that was accomplished. Perhaps He would have simply stopped births. Or allowed the people to colonize other planets. Or just made Earth bigger.
If we believe God is perfect and sovereign and all-powerful, we have to believe He had a plan, and that it was sufficient to accommodate the number of people His plan called for. After all, He Himself said that His creation, including the charge to fill the earth, was "very good" (Genesis 1:31).