No, FK,
And when they saw him, they worshipped him: but some doubted [Mat 28:16-17]
So, the Great Commission applies to the remaining Apostles, and even among them some did not believe. Where did you get "all believers" from?
Acts 1:8, “But ye shall receive power, after that the Holy Ghost is come upon you: and ye shall be witnesses unto me both in Jerusalem, and in all Judaea, and in Samaria, and unto the uttermost part of the earth.” The great commission has universally been interpreted to mean it is incumbent on all believers to make disciples. It was only after the professional class saw their influence dwindling as the masses equipped with the word of God became bold in their witness, that they took to heart the words of that great saint, Le Petomane, “We’ve gotta protect our phoney-baloney jobs, gentlemen, we must do something about this immediately!” and reinterpreted the Great Commission as speaking only to them.