Baha'u'llah may have written some things that are similar to the Qur'an but The Baha'i Faith is not based upon the Quran.
It is based on the Revelation of Baha'u'llah, which is what God revealed to Baha'u'llah.
“O KING! I was but a man like others, asleep upon My couch, when lo, the breezes of the All-Glorious were wafted over Me, and taught Me the knowledge of all that hath been. This thing is not from Me, but from One Who is Almighty and All-Knowing. And He bade Me lift up My voice between earth and heaven, and for this there befell Me what hath caused the tears of every man of understanding to flow.”
Since Baha'u'llah received His knowledge from God, he did not have to read the Old or New Testaments. I don't know where Abdu'l-Baha got his knowledge of the Bible. He may have read it but he also got a lot of knowledge from his father.
A per the Qur'an, Baha'u'llah was raised as a Muslim so He knew the Qur'an very well.