The short answer is NO. Angels are beings created by God (Colossians 1:15-17) and are entirely different from humans. They are God’s agents to carry out His plan and to minister to the followers of Christ (Hebrews 1:13-14). There is no biblical evidence that angels were formerly humans or anything else—they were created as angels. Angels have no need of and cannot experience, the redemption that Christ came to provide for the human race. 1 Peter 1:12 describes their desire to look into the Gospel, but it is not for them to experience. Had they been formerly humans, the concept of salvation would not be a mystery to them, having experienced it themselves. Angels rejoice when a sinner turns to Christ (Luke 15:10), but salvation in Christ is not for them.
Eventually, the body of the believer in Christ will die. The spirit of the believer goes to be with Christ (2 Corinthians 5:8). The believer does not become an angel. Elijah and Moses were recognizable on the Mount of Transfiguration. They had not transformed into angels, but appeared as themselves—although glorified—and were recognizable to Peter, James and John.
In 1 Thessalonians 4:13-18, Paul tells us that believers in Christ are asleep in Jesus; that is, their bodies are dead, but their spirits and souls are alive. This text tells us that when Christ returns, He will bring with Him those who are asleep in Him, and then their bodies will be raised, made new like Christ’s resurrected body, to be joined with their spirits which He brings with Him. All believers in Christ who are living at the return of Christ will have their bodies changed to be like Christ, and they will be completely new in their spirits, no longer having a sin nature.
All the believers in Christ will recognize one another and live with the Lord thereby. We will serve Him throughout eternity, not as angels, but along with the angels.