No. The church of God is not the kingdom of God. The church of God is INSIDE the kingdom of God. You see, the kingdom of God is bigger than the church of God.
Col 1:13 He has delivered us from the power of darkness and conveyed us INTO the kingdom of the Son of His love
The apostle Paul here is writing to the called out ones of God (the Church of God) and he says that they were delivered from the power of darkness and conveyed, transferred and carried INTO the kingdom of the Son of His love.
The kingdom is something that they were conveyed INTO. The preposition signifies movement towards the interior or inner parts. It simply means entry. The kingdom is something that the Church entered into.
Take a look at another verse to make it more clear and plain:
2Pe 1:11 for so an ENTRANCE will be supplied to you abundantly INTO the everlasting kingdom of our Lord and Savior Jesus Christ.
Peter, speaking of the future aspect of the kingdom, is writing to the called out ones of God (Christians or the Church of God) and he says that the kingdom is something that they will have an entrance into.
These verses (Col. 1:13 and 2 Pet. 1:11) speak of the Church entering the kingdom. If the Church is the kingdom, then why does she have to enter into the kingdom since she herself is the kingdom?
You see, the Church and the Kingdom are different. The one enters into the other.
Think about it. The Church is the bride of the King, the future queen, so to speak, who will sit beside the King to reign with Him. The queen is not the King's kingdom. No, she is inside His kingdom, reigning with Him.