Only if it's a very competitive market, and even that effect will only happen over time.

Product differentiation introduces pricing power for individual firms, and depending on the style of competition you think will occur (e.g., Cournot oligopoly vs. Bertrand), you may very well never approach anything close to perfect competition with the small number of firms there are in this market.

> Though in economic theory cost should approach marginal cost

...in a perfectly competitive market. In a situation where monopoly rents can be charged (which is what having a moat is about), prices should hit the point where unit price × sales - cost is maximized.