According to the Evangelical Manifesto, I am Evangelical (denomination: Mennonite Brethren).
http://evangelicalmanifesto.com/wp-content/uploads/2016/03/Evangelical_Manifesto.pdf
There are always going to be those who are biblically illiterate from every faith persuasion. The truth is, most of us do not have the time or wherewithall to study in-depth and in context. I spent about 5 years deeply studying marriage/divorce/remarriage as it pertains to both human marriage and God's relationship with Israel and Jesus' relationship with the church. While I am not a theologian, nor have I gone to Bible school, I think I can carry on a relatively "literate" conversation about this one subject.
But... I also have always worked or gone to school. So it's not like I can study other subjects or books of the Bible that deeply and be literate in all areas. But I do know what I believe, and why I believe it. For me as an Evangelical, I am more concerned with my relationship with the Father and the Son and the Holy Spirit than I am about theological knowledge. I want to know Jesus, not just get busy interpreting and framing the Word in a way that makes the most sense, because some might argue that it is non-sensical anyway, given that it is not in its original language, cultural, or political context.
I don't know of any studies that can refute or back up the claim that Evangelicals are biblically illiterate. I believe we are all biblically illiterate, at least to one degree or another.