Twill for formal shirting? Yes.
Twill fabrics are easily recognisable because of the diagonal weave structure. The diagonal effect can vary from very fine, subtle twills to much larger like Imperial or Cavalry twills. Twills will almost always have a little sheen, although the degree may depend on the fabric, color and cotton used. Twill is an extremely dense weave that can be obtained in extremely high thread numbers, some of which can be confused with silk.
Due to the diagonal structure, twill is a little softer than broadcloth and drapes more easily. Twill doesn't give you the same "crisp" look as a freshly pressed broadcloth can, but it is relatively easy to iron and resists wrinkles.
We choose twill for slightly more formal look together with sharp tailoring in fine wool and a tie.