Certainly, although I would do it a bit differently.
1. First, the capital isn't really in the northeast, but rather at the point where the north meets the south. I would have Twilight represent New England specifically because of its high concentration of prestigious universities.
2. Rather than Rarity representing the southwest (I assume you meant southwest), I would have her represent the region between (and including) New York and DC (and maybe the Tidewater region as well) because Rarity has a 'Mid-Atlantic' accent, and her frequent visits to Manehattan in the show for both business and pleasure.
3. Applejack is strange because, despite having a southern accent and essentially being a stereotypical southerner, both the state most associated with growing apples and the region where Johnny Appleseed lived are in the north. Although people tend to see her as a southerner first and an apple farmer second.
4. Rainbow Dash being a narcissist would fit California well. Her being in the Wonderbolts would also fit the California/Nevada region well because of the high concentration of military bases there, while the Northwest has very few significant bases outside of Seattle.
5. Other regions like Hawaii, Alaska, Plains, and the Rust Belt are left without adequate representation, so we should look at other ponies beyond the mane six to fulfill that.