Does the text in John 1:9 support the Arminian theory of “universal prevenient grace”?

The proponents of man’s “free will” conditional redemption often use John 1:9 as one of their favourite proofs in support of their doctrine of “universal prevenient grace”, according to which God gave to all men without exception a measure of grace to make it possible for them to come to Christ of their own “free will” and thus obtain salvation. Is this however what the Scripture teaches?