Nope.
In Acts 1:20-22, Peter specified two qualifications for the appointed apostle in replacement of Judas.
The replacement had to be someone who 1) had accompanied the disciples from the beginning of Jesus' ministry and had seen what the apostles had seen and heard what they have heard, an eyewitness to the miracles and teachings of Jesus; 2) was an eyewitness of Jesus' resurrection.
Acts 1:20-22
20 “For it is written in the Book of Psalms:
‘Let his dwelling place be desolate,
And let no one live in it’;
and,
‘Let another take his office.’
21 “Therefore, of these men who have
accompanied us all the time that the Lord Jesus went in and out among us, 22
beginning from the baptism of John to that day when He was taken up from us, one of these must become a
witness with us of His resurrection.”
When James was killed (Acts 12:2), no replacement was chosen for him. Why? I believe the answer is in Acts 1:20 above. In fact, Peter applied Psalm 69:25 that speaks about the removal of the enemy (Judas) and psalm 109:8 that mentions the replacement of the enemy by someone else (Matthias). This means that Judas was replaced because he abandoned the position, which was not the case of James who died as a faithful martyr.
In Matthew 19:28, Jesus indicated that the twelve apostles will judge the twelve tribes of Israel. Twelve apostles, twelve tribes.