Isn't General Relativity directly implied by the concept of Universal Gravitation itself?

Now I'm speaking in very general terms here, and am perhaps being too vague. But, when Isaac Newton felt the apple fall on his head, he had a revelation. Maybe Aristotle was wrong, and objects didn't just fall to earth. Maybe all objects fall to all other objects! He could explain the entire universe that way. But doesn't the concept of Universal Gravitation itself imply that a massive enough object could make everything around it fall to itself so absolutely that nothing around it could ever occur again; that is, wouldn't a powerful enough gravitational force necessarily stop time? So, isn't General Relativity and concepts like Black Holes directly implied by Newton's original work? If so, why does Newton assume that space is "absolute". Isn't that concept inconsistent with the direct implications of Universal Gravitation itself?