And if you search for "web browsers" on Bing IE doesn't show up at all except in a side bar under 'related searches'. Seems MS hasn't done any SEO for IE under the term 'web browser'.
But if you're using IE, you're using IE, and there's no need to search for it.
And if you're not using IE, then you're either on a platform which IE doesn't run on, or you (or your friendly BofH) have already taken steps to not be running IE. For either of those cases, you wouldn't be helped by searches for "web browser" listing IE highly.
So any outlay of resource on SEO would be wasted.