Sorry, it's a pleasing idea, but no.
The Sagittarius Dwarf has nothing to do with the Sagittarius arm: its central portion just happens to lie in the same direction as the Sag arm, but it's on the far side of the galaxy from us. It's trailing a big sparse spiral of stars as it is tidally disrupted by the Milky Way, but that spiral doesn't follow the spiral structure of our galaxy, as the diagram on the linked page shows: instead, it arches out of the galactic plane and then drops back in again at around our location.

Grant Hutchison