The stage is set for the Battle of Armageddon in Revelation 16:12-16:
12 The sixth angel emptied his bowl on the great river Euphrates. Its water was dried up to prepare the way for the kings of the East. 13 I saw three unclean spirits like frogs come from the mouth of the dragon, from the mouth of the beast, and from the mouth of the false prophet. 14 These were demonic spirits who performed signs. They went out to the kings of the whole world to assemble them for the battle on the great day of God the almighty. 15 (“Behold, I am coming like a thief.” Blessed is the one who watches and keeps his clothes ready, so that he may not go naked and people see him exposed.) 16 They then assembled the kings in the place that is named Armageddon in Hebrew.
No description of the battle follows until Revelation 19:11, 12, 17-21 (assuming that this refers to Armageddon):
11 Then I saw the heavens opened, and there was a white horse; its rider was [called] “Faithful and True.” He judges and wages war in righteousness. 12 ... He had a name inscribed that no one knows except himself. ... 17 Then I saw an angel standing on the sun. He cried out a loud voice to all the birds flying high overhead, “Come here. Gather for God’s great feast, 18 to eat the flesh of kings, the flesh of military officers, and the flesh of warriors, the flesh of horses and of their riders, and the flesh of all, free and slave, small and great.” 19 Then I saw the beast and the kings of the earth and their armies gathered to fight against the one riding the horse and against his army. 20 The beast was caught and with it the false prophet who had performed in its sight the signs by which he led astray those who had accepted the mark of the beast and those who had worshiped its image. The two were thrown alive into the fiery pool burning with sulfur. 21 The rest were killed by the sword that came out of the mouth of the one riding the horse, and all the birds gorged themselves on their flesh.
Human souls are not described as being directly involved. However, they are indeed mentioned as interested parties.
Revelation 6:9-11 NABRE
9 When he broke open the fifth seal, I saw underneath the altar the souls of those who had been slaughtered because of the witness they bore to the word of God. 10 They cried out in a loud voice, “How long will it be, holy and true master, before you sit in judgment and avenge our blood on the inhabitants of the earth? 11 Each of them was given a white robe, and they were told to be patient a little while longer until the number was filled of their fellow servants and brothers who were going to be killed as they had been.
Summary: As others have pointed out, the battle may be symbolic. This seems especially likely in that the enemies of God are nearly all killed by the sword that comes out of the mouth of the Rider, probably representing God's word. However, the battle's literal description implies that it takes place on earth, where rivers are dried up to make way for eastern kings and birds devour the flesh of the losing army. Spiritual forces are certainly at work, but there is no direct mention of human souls being involved except as passionately interested watchers.
Conclusion: there is no mention of human souls being directly involved in the battle of Armageddon.