"Yet in this case, as in so many others, was proved the truth of Paul's assertion that the weapons of his warfare were “mighty through God to the pulling down of strongholds,” 2 Corinthians 10:4 . Even in Nero's household, trophies of the cross were won. From the vile attendants of a viler king were gained converts who became sons of God. These were not Christians secretly, but openly. They were not ashamed of their faith. AA 463.1 And by what means was an entrance achieved and a firm footing gained for Christianity where even its admission seemed impossible? In his epistle to the Philippians, Paul ascribed to his own imprisonment his success in winning converts to the faith from Nero's household. Fearful lest it might be thought that his afflictions had impeded the progress of the gospel, he assured them: “I would ye should understand, brethren, that the things which happened unto me have fallen out rather unto the furtherance of the gospel.” Philippians 1:12 . AA 463.2"
"(For the weapons of our warfare are not carnal, but mighty through God to the pulling down of strong holds;)"
The EGW passage directly quotes 2 Corinthians 10:4 and applies it to Paul's ministry, making it a clear and explicit allusion.
"But I would ye should understand, brethren, that the things which happened unto me have fallen out rather unto the furtherance of the gospel;"
Ellen White directly references Philippians 1:12 in this passage.
"When the Christian churches first learned that Paul was to visit Rome, they looked forward to a signal triumph of the gospel in that city. Paul had borne the truth to many lands; he had proclaimed it in great cities. Might not this champion of the faith succeed in winning souls to Christ even in the metropolis of the world? But their hopes were crushed by the tidings that Paul had gone to Rome as a prisoner. They had confidently hoped to see the gospel, once established at this great center, extend rapidly to all nations and become a prevailing power in the earth. How great their disappointment! Human expectations had failed, but not the purpose of God. AA 463.3"
"But the Lord said unto him, Go thy way: for he is a chosen vessel unto me, to bear my name before the Gentiles, and kings, and the children of Israel:"
Both passages relate to the idea of God's plan being fulfilled even when human expectations are not met. Acts 9:15 speaks of Paul being chosen to bear God's name before kings, while the EGW passage describes the initial disappointment of the churches when Paul went to Rome as a prisoner, but ultimately God's purpose was still fulfilled.