No, this is not what the Bible means by eternal life. Eternal life is life on a completely different level, because it means living in God's presence in heaven forever. This life is only temporary, but heaven is eternal, and now we "wait for the mercy of our Lord Jesus Christ to bring (us) to eternal life" (Jude 1:21).
Nor does the Bible promise that someday we will overcome every disease and sickness on this earth. I'm very thankful for all the advances that have been made in medicine during my lifetime; I wouldn't be alive today if it weren't for some of them. I'm thankful too for the dedicated men and women who are involved in medical research; God has given them their abilities, and He wants them to be used for our benefit.
But disease and sickness will be with us until the end of time, as will accidents and other things that cause death. Life is fragile; no one knows how long or how short their life will be. The Bible says, "What is your life? You are a mist that appears for a little while and then vanishes" (James 4:14).
This is why we need to turn to God and commit our lives to Christ while we can. Have you opened your heart and life to Him? Don't let another day go by without making your commitment to Christ—for He alone can give us the gift of eternal life.