"Christ does not drive but draws men unto Him. The only compulsion which He employs is the constraint of love. When the church begins to seek for the support of secular power, it is evident that she is devoid of the power of Christ—the constraint of divine love. MB 127.1"
"No man can come to me, except the Father which hath sent me draw him: and I will raise him up at the last day."
Both passages discuss the concept of being 'drawn' to Christ. While EGW doesn't directly quote John 6:44, she uses the same imagery and concept to illustrate a similar point about God's method of leading people.
"But the difficulty lies with the individual members of the church, and it is here that the cure must be wrought. Jesus bids the accuser first cast the beam out of his own eye, renounce his censorious spirit, confess and forsake his own sin, before trying to correct others. For “a good tree bringeth not forth corrupt fruit; neither doth a corrupt tree bring forth good fruit.” Luke 6:43 . This accusing spirit which you indulge is evil fruit, and shows that the tree is evil. It is useless for you to build yourselves up in self-righteousness. What you need is a change of heart. You must have this experience before you are fitted to correct others; for “out of the abundance of the heart the mouth speaketh.” Matthew 12:34 . MB 127.2"
"For a good tree bringeth not forth corrupt fruit; neither doth a corrupt tree bring forth good fruit."
Ellen White directly references Luke 6:43 in this passage.
"O generation of vipers, how can ye, being evil, speak good things? for out of the abundance of the heart the mouth speaketh."
Ellen White directly references Matthew 12:34 in this passage.