My eyes don't do that. I look at all the words first - the narration, then the dialog, then any sound effects, and then I look at the picture to make sense of it all. In a simple comic, this is not a problem:
My other difficulty comes with panels that contain no words - no narration, no dialog, nothing. My brain has to "write" its own narration so that I can be sure I understand what's going on. And I don't always read a character's emotions correctly, especially in manga.
For example, the "grumpy cat" memes don't make sense to me. This cat does not look grumpy; to me, s/he looks like s/he's about to cry. So when I see a cat that everyone thinks is grumpy and my brain says "sad" instead of grumpy, imagine how complicated a manga can be, when a character's emotions could be demonstrated with a "thought cloud" above their head containing a punctuation mark. [I looked for a decent example of this online and could not find one.]
Perhaps this is why comic books and graphic novels have gotten such a bad rap from teachers, parents, and the like. A person who does not regularly read graphic works may not understand that it takes a different kind of literacy to understand and read those works; learning to read a comic book is quite different from learning to read a print book.
As I write this, I am watching episode two of the second season of Warehouse 13; the episode deals with comic book superheroes come to life. The main character who is generally considered more intelligent is not able to help much because she hasn't read comic books; at the beginning of the episode, she teases her partner for having read comic books as though they are "less than;" by the end of the episode it is clear that reading graphic works, while different from reading print works, is still valuable.
It's clear that, as a future public librarian, I need to continue to develop my graphic literacy.