No it doesn't. The idea of no death is barely plausible but not supported by the text. The idea of a "fall" is directly contradictory to the text.
To be fair to Faith, Scripture does support her assertion. You have to go to the book of Romans, chapter 5 to find it though. In the passage the author is comparing Adam's legacy to that of Jesus. " Wherefore, as by one man sin entered into the world, and death by sin; and so death passed upon all men, for that all have sinned..." I don't have the whole passage memorized, but you see the point.
This is where the hucksters like Ken Ham and Kent Hovind say the lions, hyenas, and T-Rex were vegetarian; because to be a carnivore you have to kill, but there is no death yet. Although plants are also living things that must be destroyed for the continued survival of another. So, weird thing that.
"...heck is a small price to pay for the truth"