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Biblical unitarians (BU's) are a collection of people who combine a strong view about the Bible with a view that the Bible does not teach that God is more than 1 person, and therefore that Jesus is not God. Rather, the Father is God.
Although unitarianism impinges on various other theological beliefs in various ways, I don't think it effects this one directly. As with standard trinitarian belief, BU's would hold that Jesus is without sin. See 1 Peter 1:19 ("the precious blood of Jesus Christ, a lamb without blemish or defect"), 2 Corinthians 5:21 ("who knew no sin"), Hebrews 4:15 ("one who has been tempted in all things as we are, yet without sin"), 1 John 3:5 ("in Him there is no sin"), and so on.
As the BU article Jesus is the Son of God, not God the Son says
"He is the only begotten Son of God, who loved so much that he lived a sinless, obedient life and died on the cross for us[.]"
However, BU's would hold that Jesus could sin as He is a man, which would distinguish them from some trinitarians who hold that Jesus can't sin as He is God, as in the article Was Jesus sinless? where it states
"[A]s Jesus Christ is God, He has no capacity to sin."