Is it scriptural to say, "Come to God just as you are?"
Yes, but a better way to say it would be to "trust in Jesus as your Savior." We come to the Father through His Only Begotten Son.
Act 4:12 Neither is there salvation in any other: for there is none other name under heaven given among men, whereby we must be saved.
We cannot clean ourselves up before we come to God. One must come to God as he is but with a humble heart. The key is humility. When the Lord Jesus spoke the parable of the Pharisee and the sinner, He was showing us that humility before God is essential. See, both prayed to God but only the sinner was heard. The sinner received forgiveness because he knew that Only the Lord could save him. He was humble in knowing that he could not improve himself but instead asked God to "have mercy on me." So each sinner must come to Jesus as they are, acknowledging that they are sinners in need of the Savior-- and that He is the Only One who can save them and cleanse them from their sins. It is Jesus alone who purchased our redemption by shedding His precious blood upon the Cross and therefore it is only though Him that man can be saved. We cannot bring anything to the table. One cannot trust in his own good works to be saved but rather must put his complete trust in the Lord Jesus Christ and His finished work. So we come to Christ as we are but without one plea.
Just as I am, without one plea, But that Thy blood was shed for me, And that Thou bidst me come to Thee, O Lamb of God, I come, I come.
And as the beloved hymn, "Rock of Ages" states:
Nothing in my hand I bring, Simply to Thy cross I cling; Naked, come to Thee for dress; Helplees, look to Thee for grace; Foul, I to the fountain fly,-- Wash me, Savior, or I die!
Acts 16:30-31 And brought them out, and said, Sirs, what must I do to be saved? And they said, Believe on the Lord Jesus Christ, and thou shalt be saved, and thy house.