In some ways, I think it would. Browsing the shelves, I came across a different edition of The Graveyard Book, by Neil Gaiman. Instead of illustrations by Dave McKean, it had illustrations by Chris Riddell. I love Dave McKean, he gave an ethereal quality to the Sandman comic books. But I was drawn into Riddell's illustrations as I flipped through the pages. The cover features the main character, Bod, and his guardian looking sleek, tall and antique. Would I have experienced the characters differently if I experienced Riddell's version first? I think so. Just considering the first page, there's a big difference. In McKean's version, there is a disembodied hand that hovers with a knife. It accompanies the famous first line of this Newbery winner, "There was a hand in the darkness, and it held a knife." Immediately I, as the reader am wondering what this knife is going to do. After all, knives sneaking around in the darkness are up to no good.
Another book cover that would have a dramatic impact on the reader is the cover to Hunger Games by Suzanne Collins. In America, the cover depicts the famed Mockingjay pin that is central to the symbolism of the story. But in Italy, this same story has a darker mood. Katniss peers out of a hood with menace. Not someone I would want to sit with in the cafeteria. Instantly, I have a preconception about the story before I've even read a word.
So in the end, do different covers and illustrations change the reading of the story? I think they do. Just in the way that the background of the readers will influence how they experience the story. These covers create impressions about the character, impressions that it is difficult for words to change. But then, that's not the purpose of words. Words lead us into places, take us into scenes or settings. How we get there and what we think once we're there... that's our own business.