Why won't SFML let me access the vertices of sf::Text?
Encapsulation, or what did you think?

But the vertices don't refer to border points of each letter, they're rather the vertices in the (rectangular) texture containing the rendered glyphs. So I'm not sure how this helps for outlines and shadows.
To achieve those effects, you could either use a shader, or render modified versions of the text in advance. For example, a shadow can be achieved by a black half-transparent text, and an outline by 4 texts, each of which is shifted by 1 pixel in another direction.