Yeah it definetly would. Death is an important part of life. Basically, life can't continue to exist without death. Anyways, if humans really do find the secret to immortality, it would probably be kept a secret. I mean who's to say we haven't found the secret already? I'm sure if immortality is achieved, only a select few will enjoy it.
Just look at the life cycle: An organism lives its entire life feeding on organisms lower in the food chain and then it dies. When it dies, decomposers feed on its body and return nutrients into the earth. These nutrients give life to plants. And the cycle continues.