Definitely. You seem to have understood the main message of this story completely. What is so significant about the image of the woman who is trapped behind the yellow wallpaper, with the black lines acting as bars, is that it is a projected image of how the narrator herself feels and how she is treated by society and her husband. Note the way that she protests about the fact that she is forced to stay in this room and rest, even though she herself would like to go out and have some sort of mental stimulation. The figure of the woman and the yellow wallpaper itself therefore symbolises the way that she as a woman, and women in general in this patriarchal world, are restricted and trapped. Notice the following description:
And she is all the time trying to climb through. But nobody could climb through that pattern--it strangles so; I think that is why it has so many heads.
They get through, and then the pattern strangles them off and turns them upside down, and makes their eyes white!
The woman behind the wallpaper symbolises the narrator and her feelings of being trapped and unable to go out. The black lines of the pattern symbolise the way in which patriarchal society, in this case the narrator's husband, forces women to live restricted and unfulfilled lives and mercilessly subjugate women to accept this passive role that is akin to being a prisoner. What is far more disturbing is how the narrator, by the end of the story, assumes the role of this woman and is literally trapped behind the wallpaper herself.