The short answer: No. A benefit corporation, like a normal stock corporation, cannot have tax exempt status because it has owners (aka shareholders) and because it uses the majority of its profits to benefit those owners. For those reasons, a benefit corporation will not be approved as a 501(c)(3) entity that can offer charitable tax deductibility to its donors.
If you want your entity or organization be tax exempt, you need to form a non-stock corporation. And one tip: be sure you do not use the State Corporation Commission online eFile formation service for your non-stock corporation because it will not contain the provisions the IRS requires and you'll have to do it over.