No. Philippians 2:12 teaches that a believer should work to complete his own salvation.
Paul works, presses on. He beats his body, figuratively, meaning he consciously controls his selfish impulses (1 Corinthians 9:27).
The reason people think faith is only agreeing with God about a statement He makes is that the word is translated today as "believing" when, at the time it was written, it meant "being loyal". This article is based on the content of his book by Andrew J. Wallace, a lexicologist, with whom I have had discussions on another website:
The Meaning of Faith
Perhaps the single greatest issue of theology in the present day is our understanding of “faith”. I will argue here that “loyalty” is the best translation of it and that, as such, it is totally inseparable from works and essentially means the same thing.
Outside of the Bible, what is the Greek word for faith (pistis) used to mean? We're in luck... the first century Jewish historian Josephus uses it in his writings.
In his autobiography, Jospehus describes a time when he was the leader of a small army, and another group had tried to kill him. Josephus captures the enemy leader and says to him “repent and have faith in me hereafter” (Life 110). What Josephus clearly means by this is “become part of my army, and obey my commands.”
Later he speaks of a city that had turned against him, which after he has forced them into submission again, he rebukes them for revolting “from their faith in me” (Life 167). Again, he's speaking of their loyalty to him.
What exactly is the quality that Josephus is getting at? Think about his usage of the word in an army and the concept of soldiers following their leader. What is the relationship between a soldier and their commanding officer like? The solider is loyal and trusting, he follows his superiors' commands, when the captain leads the charge into battle the soldier is right there behind him following in his footsteps. The concept is one of “followingness”, obedience to orders, loyalty, faithfulness, allegiance etc. English is really missing a word to describe this quality of a soldier... the quality of “followingness”.
Another approach to finding the meaning of the word is to look for synonyms. Where in the Bible is a sentence used that could well have contained the word “faith”, but instead contains another word in place of it? If we look for synonyms, we find that the major synonyms used time and again are “obedience” and “follow”. Notably “belief” is never used as a synonym. Greek contains several words for intellectual beliefs and to the best of my knowledge not once are any of them used as synonyms for “faith”.
Here are some of the uses of these synonyms:
Lu 11:28 But he said, "Blessed rather are those who hear the word of God and obey it!"
Ac 5:32 “And we are witnesses to these things, and so is the Holy Spirit whom God has given to those who obey him."
Ro 2:8 “while for those who are self-seeking and who obey not the truth but wickedness, there will be wrath and fury.”
2Th 1:8 “in flaming fire, inflicting vengeance on those who do not know God and on those who do not obey the gospel of our Lord Jesus.”
Heb 5:9 “and having been made perfect, he became the source of eternal salvation for all who obey him”
1Pe 4:17 “For the time has come for judgment to begin with the household of God; if it begins with us, what will be the end for those who do not obey the gospel of God?”
Ro 6:16 Do you not know that if you present yourselves to anyone as obedient slaves, you are slaves of the one whom you obey, either of sin, which leads to death, or of obedience, which leads to righteousness?
Ro 15:18 For I will not venture to speak of anything except what Christ has accomplished through me to win obedience from the Gentiles, by word and deed,
Ro 16:19 For while your obedience is known to all, so that I rejoice over you, I want you to be wise in what is good and guileless in what is evil.
2Co 7:15 And his heart goes out all the more to you, as he remembers the obedience of all of you, and how you welcomed him with fear and trembling.
2Co 9:13 Through the testing of this ministry you glorify God by your obedience to the confession of the gospel of Christ and by the generosity of your sharing with them and with all others,
Mt 4:19 And he said to them, "Follow me, and I will make you fish for people."
Mt 10:38 and whoever does not take up the cross and follow me is not worthy of me.
Joh 10:4 When he has brought out all his own, he goes ahead of them, and the sheep follow him because they know his voice.
Joh 10:27 My sheep hear my voice. I know them, and they follow me.
Joh 12:26 Whoever serves me must follow me, and where I am, there will my servant be also. Whoever serves me, the Father will honor.
Ac 5:37 After him Judas the Galilean rose up at the time of the census and got people to follow him; he also perished, and all who followed him were scattered.
1Ti 5:15 For some have already turned away to follow Satan.
1Pe 2:21 For to this you have been called, because Christ also suffered for you, leaving you an example, so that you should follow in his steps.
2Pe 1:16 For we did not follow cleverly devised myths when we made known to you the power and coming of our Lord Jesus Christ, but we had been eyewitnesses of his majesty.
In short “faith” is following an example, command, or person. It is loyal allegiance and obedience.
Since the Reformation there has been a concerted attempt to separate faith from works because of a reading of Paul that misunderstood his condemnation of works of the law as being a condemnation of all human effort toward salvation, and so it was thought that Paul was contrasting mere belief in God (“faith”) against human attempts at righteousness through “works”. If we accept that this is a misreading of Paul, and accept that faith itself refers to obedience and loyalty, then it breaks the faith vs works dichotomy.
Can someone obey without doing any works? If they are "saved by obedience" is it their obedience that saves them or their works done in obedience? Clearly that is not a sensible question: To speak of obedience apart from works is absurd and it is equally reasonable both to speak of them being saved by their works and of them being saved by their obedience because the two are totally inseparable. If Christ leads the way through a forest, someone can hardly follow Christ without putting one foot in front of the other and walking in the footsteps of Christ. Their walking gets them out of the forest, and following Christ gets them out of the forest, it's merely two ways of describing one and the same thing. You can call it “works” or you can call it “faith”, and you're still talking about the same thing. If someone is prepared to follow Christ out the forest they are as good as out of the forest already, the rest is merely a matter of time: Their attitude is all that matters.