Yes. All diamonds sparkle and the Asscher cut is no different. However, the open facets lend themselves to a different type of sparkle than cuts with diagonal facets. Expect longer flashes of bright light instead of the glitzy sparkle of cuts such as the round brilliant or oval cut.
It’s also important to remember that cut isn’t the only factor in a diamond’s sparkle level. Sparkle comes from how well the diamond refracts and reflects light, and while the facets in each cut play a major role in this, the stone’s overall quality is also a factor.