When someone is led to Christ by someone using a particular version, doesn't that mean that version is God's word?
No. Modern Bible versions certainly contain portions of God's word. However, if you read an NIV and get saved, that does not mean that the NIV is correct when it claims that Elhanan killed Goliath (2 Sam. 21:19, NIV), neither does it justify changing "God was manifest in the flesh" to the JW-friendly "He appeared in a body" (1 Tim. 3:16 NIV).
Paul wrote under the inspiration of the Holy Spirit that "we know that all things work together for good to them that love God, to them who are the called according to his purpose." (Romans 8:28).
Further, we see in the Old Testament that even though Moses disobeyed God and struck the rock a second time, the people were still allowed to drink (Numbers 20), showing that God can work around the disobedience of his people. Notice, though, that Moses was himself denied a blessing because he "believed not," so this is by no means an excuse to continue promoting the use of corrupt versions.
On a related note, it is also wrong to say that the KJV is God's word "because" someone was saved reading it. See below.
The following is from Sam Gipp's The Answer Book.
QUESTION: Someone said, "The King James Bible is the Word of God because I got saved through it!" Is that statement correct?
EXPLANATION: The Bible is infallible and perfect without any influence by any sinner. By accepting Christ as our personal Saviour we impart nothing to Scripture, though God imparts eternal life to us.
Many have been led to Christ by someone using other versions. I once spoke with a man who vehemently claimed that the Good News for Modern Man version was the infallible word of God because someone had led him to Christ using it. Wrong! His getting saved through a Good News for Modern Man did not correct so much as one of the many gross inaccuracies in that version.
I have a friend who believes the Bible (KJV) to be the infallible, perfect word of God. Yet he himself was led to Christ by someone using a Living Bible. Did the Living Bible become the infallible Word of God the moment he believed? Of course not. It never was perfect and never will be. But if it did become perfect because he got saved through it, would it not have lost its perfection when he chose to use the King James?
So we see that the Bible, King James of course, is the infallible, perfect word and words of God regardless of what someone used to lead you or me to Christ. In fact, it would still be the perfect infallible word and words of God, even if we hadn't gotten saved at all.