That would not be convincing, no.
Suppose the Bible verifiably had the complete plans to an operational nuclear fusion reactor, that is been unchanged since the Bible was written about two thousand years ago.
What conclusion could we draw from that? Most people immediately would conclude that it was divinely inspired... but is that the only possibility?
If we can assert that a universe-creating being, outside of space and time, handed the blueprints to the Bible authors, could we not also assert that aliens made the contribution? What about an ancient unknown technologically advanced human civilization - like the Lost city of Atlantis - that has since been erased from history?
Why are you choosing the first possibility over the others?
Many people engage in a "process of elimination" approach to understanding reality, but the list that is being crossed-off are a limited set of possibilities that the person thinks is possible. Often in science, the actual real answers were ones we didn't even consider, and were a surprise to us.
It is not a great way to investigate reality.
All we can say, for the fusion reactor plans in the Bible, is that "somehow, the Bible authors gained access to advanced scientific knowledge", and any further details as to from where, or from whom, require extra evidence to establish. It seems silly to us to pick the possibility with the most assumptions, violating the most of known reality, as the answer for no good reason.
Scientific knowledge in the Bible is not unprecedented. We're occasionally confronted with Hebrews 11:3:
Through faith we understand that the worlds were framed by the word of God, so that things which are seen were not made of things which do appear. - KJV
By faith we understand that the universe was formed at Godís command, so that what is seen was not made out of what was visible. - NIV
The Christian will assert that this is talking about particles or atoms, long before modern science figured it out. Unlike the unambiguous fusion reactor plans mentioned before, these verses are extremely vague, and open to interpretation.
Atoms aren't invisible. Most everything you're looking at is made of atoms, which you can see... just a whole bunch of them at once. What they should have said is that an individual atom is invisible to the naked eye. Instead of a description so far off the mark, it could have used an allegory to a stone wall that is made up of individual stones, except these stones are too small to see individually. Why is the verse so vague? On top of that, when read in context with surrounding verses, one could make the argument that it is talking about God, not atoms.
If that was not damning enough, those people who make this particular argument were unaware that the Greeks were pondering the existence of atoms (as well as named the concept) before 370BC, about 420 years before the Book of Hebrews was written (about 65AD). Like in our hypothetical fusion reactor example, this other possibility was not even considered by these Christians.
The few examples in the Bible where it says the Earth is a sphere is cherry picked (ignoring the verses that clearly make it out to be flat), fail in the same way. Another Greek, Eratosthenes, before 200BC, not only concluded the Earth was a sphere, but used math and a stick to estimate the Earth's circumference to within 17% accuracy. 
... but the apologists didn't realize humans had the ability to infer/investigate these facts during the time of the Bible. So why do we need to invoke magic to explain it?
For the reasons above, this is why atheists do not find such arguments compelling. We don't find the apologists have applied critical thinking, and for unknown reasons, have chosen the single most absurd possibility (God) to explain something that often has much more reasonable explanations.
Even if we had no other known possibilities, that does not mean the idea you've asserted is true automatically. You still have to demonstrate it, because the real answer could still be unknown to us, even as a basic possibility.
If you don't mind a question in return, here's one to consider for yourself.
If you consider parts of the Bible that are consistent with science to be evidence of the Bible's divinity, do you also consider parts of the Bible that gets the science clearly wrong as evidence against its divinity?
If you rationalize away the parts it gets wrong, saying "it is allegory" or "out of context", etc, have you considered that you may be engaging in Confirmation Bias?