What a timely and thoughtful question for me right now, thank you.
I am currently in the book of Job where God is finally talking directly to him (Chapter 38). He reveals to Job that, no matter how much science you think you know, God has infinitely more knowledge. Man, that just puts me in my place every time I read it.
To your question, it really doesn't matter what we think we've accomplished as human beings. In every instance, from curing Polio, to landing on the moon, God was the one who made it happen.
So, the short answer is yes, if the medical community found a way to extend human life indefinitely, the only way it could ever happen is if God willed it. But, I think you'll find that most people on this forum, including myself, would find that scenario highly unlikely, due to the problem of sin, as explained in Genesis.
Still, God allows anything to happen at any time to anyone for whatever reason He chooses. If that doesn't instill in us a healthy fear of Him, I don't know what will. Revisit the book of Job, and you'll see what I mean.