Do Michael and His angels "overcome" the Devil and his angels by the "blood of the Lamb?"
Answer: Yes. But first, some major caveats.
On the surface, most (understandably) construe Revelation 12:4 as demonstrating that God cast Satan and one-third of the angels from heaven, just as the verse reads:
Revelation 12:4: "And [the great red dragon with 7 heads, 10 horns, 7 diadems]'s tail swept away a third of the stars of heaven and threw them to the earth. And the dragon stood before the woman who was about to give birth, so that when she gave birth he might devour her child."
Let us understand what is being conveyed here. The "third of the stars of heaven" being cast out likely represent the struggle taking place among the principalities and powers of Roman civil government instigated by Satan, something that would be witnessed worldwide.
Fiery red symbolizes ravenous death; seven heads (Rome was the "City on seven hills") show great reasoning among the political echelon; ten horns demonstrate a shared monopoly among the ten Roman kings at the time -- all in turmoil. Diadems are often representative of temporary authority.
Satan's tail casting down these stars is a figure of his purging any rulers that stood in his way. Lastly, "the woman" is first, the nation of Israel who would give birth to the Messiah, and later the Church. Whether physical or spiritual, "Israel" is the chosen of God.
Now, Michael was the “Great Prince who [stood] guard over the sons of [Daniel’s] people” (Dan. 10:13, 10:21, 12:1). It is a fact that Daniel’s people were the Israelites, those protected by Michael. Further, we also know that it was Christ Who was the rock that followed and protected [stood guard over] them in the wilderness (1 Cor. 10:4). Michael is the key that binds everything together here.
Jude vs. 9: “But Michael the archangel, when he disputed with the devil and argued about the body of Moses, did not dare pronounce against him a railing judgment, but said, ‘The Lord rebuke you!’”
Many understand that the Angel of the Lord -- and in this case, simply "the LORD" is, in fact, the "Preincarnate Christ." Therefore, "Michael" is the One "arguing" with Satan. What are they arguing over? "The body of Moses." How so? Well, just as Christians under the New Testament are the "body of Christ," so too was ancient Israel under the Old Testament, or "body of Moses" (cf. Heb. 3:5-6).
Joshua, the high priest (Zech. 3:4) was standing in filthy garments (sin), representative of the body of Moses: Israel. "Michael" and Satan were disputing Israel's salvation (Zech. 3:2c):
Zechariah 3:2: The LORD said to Satan, “The LORD rebuke you, Satan! Indeed, the LORD who has chosen Jerusalem rebuke you! Is this not a brand plucked from the fire?”
Since we know from Jude vs. 9 that Michael argued with Satan, and we know from Zech. 3:2 that the LORD proclaimed exactly the same (we find this nowhere else in Scripture), we can safely presume that both the LORD of Zech. 3 and the "Michael" of Jude vs. 9 are one and the same: Christ, the LORD.
Thus, the “battle in heaven” was the spiritual battle waged on Earth between Christ and Satan during Jesus’ 3 ½-year ministry. As part of that battle, Jesus exorcised those possessed by demons, preached the Word to the lost, and cured many afflictions (including death). Satan tried (and failed) to murder the baby Jesus in Bethlehem:
Matthew 2:16: "[When] Herod saw that he had been tricked by the magi, he became very enraged, and sent and slew all the male children who were in Bethlehem and all its vicinity, from two years old and under..."
He also unsuccessfully attempted to undermine Christ's mission throughout. This was a spiritual battle to determine the destiny of the human race. Christ’s “angels” were likely the disciples (and perhaps certain real angels) endowed with casting out demons as in Luke's Gospel (10:17).
One verse later in Luke (10:18), Christ tells us He could (fore-)see “Satan being cast from heaven like lightning.” This would occur at the moment of His sacrificial death where He secured victory over the Devil:
John 12:31-32: “Now is the judgment of this world; now will the ruler of this world be cast out. And I, when I am lifted up from the earth, will draw all people to myself.”
The symbolic imagery of Revelation 12 is describing Christ’s earthly battle against the forces of darkness, all of which deprived Satan of his authority over death to those who would be drawn together to Him. The symbolism in the Book of Revelation is awe-inspiring!