A classical Arminian would never deny that Adam’s sin resulted in the incapacitation of any person’s free will. Classical Arminianism (as I have demonstrated in Arminian Theology: Myths and Realities) strongly affirms the bondage of the will to sin before and apart from prevenient grace’s liberating work.
Now, perhaps this is the point of the statement’s mention of “the Holy Spirit’s drawing through the Gospel.” But that, too, can be interpreted in a semi-Pelagian way. Semi-Pelagians such as Philip Limborch and (at least in some of his writings) Charles Finney affirmed the necessity of the gospel and the Holy Spirit’s enlightening work through it for salvation. What made them semi-Pelagian was their denial or neglect of the divine initiative in salvation (except the gospel message).