Specifically, Does the lack of Pilate's wickedness mean that Pilate himself is treated as a righteous man in the New Testament? The answer is a no, and here is why.
What does history do? It records events down that happened. However, historians select was is important to the audience that they are writing to.
David Pawson has described the Bible as the "Prophetic History", namely, history that is important to God.
The reason the sins of Pontius Pilate are not mentioned is not because the NT are portrayed him as righteous, but because the atrocities he committed were not relevant to the theological and historical point of the book.
To quickly touch upon Josephus:
"Now there was about this time Jesus, a wise man, if it be lawful to call him a man, for he was a doer of wonderful works, a teacher of such men as receive the truth with pleasure. He drew over to him both many of the Jews, and many of the Gentiles and when Pilate, at the suggestion of the principal men among us, had condemned him to the cross, those that loved him at the first did not forsake him and the tribe of Christians so named from him are not extinct at this day." Antiquities of the Jews - Book XVIII
Jesus is touched upon briefly, but not extensively, as presumably, Jesus was not of significant importance to Josephus, it's more of a passing remark.
Again, history only records what is important to the writer and the target audience and what they need to know. It's the same with the Bible, it only provides you with what is relevant to God and what he wants you to know.
So is Pilate presented as good? No.