"It is no part of Christ's mission to compel men to receive Him. It is Satan, and men actuated by his spirit, who seek to compel the conscience. Under a pretense of zeal for righteousness, men who are confederated with evil angels sometimes bring suffering upon their fellow men in order to convert them to their ideas of religion; but Christ is ever showing mercy, ever seeking to win by the revealing of His love. He can admit no rival in the soul, nor accept of partial service; but He desires only voluntary service, the willing surrender of the heart under the constraint of love. AA 541.1"
"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 deal with the idea that God draws people to Himself willingly, not through compulsion. The EGW passage expands on this idea by contrasting it with Satan's methods. While John 6:44 speaks of being 'drawn' by the Father, the EGW quote speaks of not being compelled, but drawn by love. The connection is thematic, but not a direct allusion.