No. Both those “in Christ” and those who have died without being reconciled to God will be physically resurrected. Death is not the end for either the believer or the unbeliever. However, the Bible does warn us of some important differences in the resurrection of those who are in Christ and those who are not.  

 What we do in this life determines the nature of our resurrection.

Marvel not at this: for the hour is coming, in the which all that are in the graves shall hear his voice, and shall come forth; they that have done good, unto the resurrection of life; and they that have done evil, unto the resurrection of damnation [condemnation] (John 5:28, 29).  

 The dead in Christ will be raised at an earlier time.

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 [precede] them which are asleep. For the Lord himself shall descend from heaven with a shout, with the voice of the archangel, and with the trump of God: and the dead in Christ shall rise first (1 Thessalonians 4:15, 16).  

 But the rest of the dead lived not again until the thousand years were finished. This is the first resurrection. Blessed and holy is he that hath part in the first resurrection: on such the second death hath no power, but they shall be priests of God and of Christ, and shall reign with him a thousand years (Revelation 20:5, 6).  

(Note: This thousand year period between the two resurrections is often called the millennium from the Latin word for thousand.)  

 The quality of our everlasting life will differ according to our relationship to Christ.

And many of them that sleep in the dust of the earth shall awake, some to everlasting life, and some to shame and everlasting contempt. And they that be wise shall shine as the brightness of the firmament; and they that turn many to righteousness as the stars for ever and ever (Daniel 12:2-3).

Only those who experience spiritual resurrection during this life, will continue to share Christ’s life through eternity.

And you hath he quickened, who were dead in trespasses and sins (Ephesians 2:1).