At the rapture, will living believers be taken before the dead in Christ rise?

No. Paul says believers who are alive and remain at the coming of the Lord shall not precede or go ahead of those who have died. The Lord Himself will descend from heaven with a shout, and the dead in Christ shall rise first in resurrection power.

Les explains from verse 15 that Paul writes by the word of the Lord: we who are alive and remain to the coming of the Lord shall not precede or go ahead of them who have died. The order is clear: the Lord Himself shall descend from heaven with a shout, the voice of the archangel, and the trump of God, and the dead in Christ shall rise first in resurrection power. So living believers are not taken before the dead in Christ rise.

1 Thessalonians 4:15

For this we say unto you by the word of the Lord, that we which are alive and remain unto the coming of the Lord shall not prevent them which are asleep.

Will believers who are alive at the coming of the Lord be raptured before those who have died in Christ?

No. The Word of the Lord declares that believers who are alive and remain until the coming of the Lord will not precede or go ahead of them who are asleep. Therefore, those alive at His coming are not raptured before those who have died in Christ.