No, (Francis) Bacon's scientific method of inductive reasoning was the rejection of Aristotle's method of deductive reasoning. Science was the product of Christian Europe, not ancient Greece.
If it wasn't why didn't the Greeks split the atom? It took us about 350 years to accomplish this feat since Novum Organum. Independent Greece lasted about that long after Aristotle's death and, of course, Aristotle's methods were adopted by the Romans and even Europe up until Bacon.
If the nuclear science was too dificult how about steamships or a smallpox vaccine?
Aristotle was certainly not stupid but you can make a case that his four elements (or the adoption by conventional wisdom that there were just four elements) may have actually held back scientific advancement. This is what I fear the extreme emotional instance on following a basically Darwinian model may do with science today.
On a related matter, did you ever consider how much better the descriptions of nature that are in the Bible hold up so much better than those of Aristotle or any other ancient work?
Even so, would you regard geometry and Aristotilian logic as being dependendent on the Zeus axiom? Your answer must be "Yes," for it is only by that same reasoning that our modern science can be said to be dependent on the God axiom.
I've never thought about it. Can you give some examples?