I believe putting God first is absolutely necessary for spiritual growth. To those who believe in God and his word, the Bible, as well as the Word come in the flesh, Jesus Christ, we are in fact instructed to put God first. God asks us to seek first his kingdom:
King James 2000 Bible (©2003)
But seek you first the kingdom of God, and his righteousness; and all these things shall be added unto you.
Trying to achieve spiritual growth without putting God first means we are relying on human effort and God says:
King James 2000 Bible (©2003)
For my thoughts are not your thoughts, neither are your ways my ways, says the LORD.
In fact, it is a form of idolatry to put anyone or anything else before God. As Creator he deserves the preeminent position in our lives, if we adhere to the teachings of the Christian faith as set forth by Jesus Christ.
Putting God first as we seek to attain spiritual growth means we conduct our lives according to God's laws, and not according to the teachings and traditions of man, many of which are in direct opposition to God's teachings. We cannot live up to God's standards through our own human effort, but only through God working in us. When we submit to God completely, he directs our thoughts and actions and helps us live our lives according to his will.
A person can grow spiritually in a variety of ways according to the Christian faith. Each way ultimately leads to giving God more control which answers this question: eventually, yes.
A person may realize their sin and emptiness and then begin the process of looking for a solution to this problem. In this process of discovery, many find God's forgiveness a fair option because humans continue to sin. God's forgiveness is always available according to the Christian bible as long as man is willing to confess sin. (1 John 1:8-9) God further looks to replace that emptiness or sin with something good that He provides, love. As a person grows through the experience of confession and forgiveness, the realization of one's own limits and God's supremacy is revealed. Therefore, God is put first.
A person may grow spiritually through prayer experiences. Since prayer by definition is indeed a conversation with and offer of praise to God, man ends with the same conclusion, God was just put first.
A person may grow spiritually through circumstance or experience in which God's majesty or power is revealed. These are often revealing circumstances which may be a near-death scenario or a modern-day miracle. The ultimate conclusion for the human is the idea that God is indeed active and participatory in the everyday workings of man. His ability to orchestrate detail results in awe from the human, who turns attention to the reality of God, thus putting Him first, at least for a time.
A final method of spiritual growth could be the reading of Scripture. Many personally grow from the morals presented in the bible, yet fail to spiritually grow. Scripture from the bible is said to be inspired by God (2 Timothy 3:16) and therefore God put it there first.
The actual type of growth cited here, SPIRITUAL, suggests the involvement of the Holy Spirit, who is the Spirit of God available to man on earth. For growth to occur this Spirit must be engaged. This puts God in the scenario no matter how the growth occurs.