No. The nuts are there purely for flavor, not for any structural reason.

Of course, they're there to add texture, too, and that's very important to some people (those who can't imagine tuna salad without celery*, for example). But if you boost the flour in your recipe, all you'll have for texture is nutless brownies that are way too dry.

*It may be shocking to a whole class of eaters, but there are people out there who do not put celery in their tuna salad.