Damn right! I was from a very poor family, but my parents let me know that I had damn sure better be at the top of the class. They read to me, helped me with my homework, and--of utmost importance--made it clear that I was EXPECTED to be at the top!
In the second grade, there were three reading groups: the blue birds, the green birds, and the red birds. I figured them out: the blue birds were the best readers, the red birds the worst. I was in the green birds. I knew I'd better get myself in the blue birds! I did. My first day as a blue bird, the teacher told me to read "to the end of the next paragraph". I had no idea what a paragraph was--but I figured it out fast, and she never knew. I made sure I was one of the top readers! I knew I'd better!
When I took an I.Q. test as a teenager, I scored off the board--way up in the stratospheric genius level.
The problem is that increasing parental involvement will simply not help a low-potential child exceed his potential. It will help him reach it, but nothing the parents can do will help him exceed his inborn potential.