No. In Aramaic, "Abba" literally means "father" (it's the cognate of the Hebrew av). It was also used as a man's first name in Second Temple times. "Son" would be bar. The name "Barabas" which appears in the Christian Scriptures means "son of Abba."
By Abba, you’re right. I got ahead of...uh, behind myself. My fault. Thank you for setting me straight.