Yes, to the extent that a component of the competitive market is unexpandable. This could be scare minerals, patents, or even just the economies of scale. Given that such scarcity exists in virtually all production, elements of a monopoly market will exist in any so-called "competitive" market.
Why is this so? Because where production is limited by capacity and capacity is scarce, then price wars can not exist. Acme sells widgets for 50 dollars. As does XYZ. Acme wants more business...so they lower their price to 30 dollars. But then they have more business than they can service. They then have a shortage...and people end up buying XYZ widgets even if they are more expensive, so Acme raises their price for rationing and we're back to where we started.
If Acme raises their price to 70 dollars, XYZ can't stay the same at 50 dollar, else they will sell out. So in this strange way, many "competitive" markets (like say oil) behave as one monopolistic entity.
Say Acme and XYZ merge...their behavior will be the same. They will not lower prices because of fixed capacity but can and will raise prices to monopolistic levels.
To the extent that factors of production can not be duplicated this will be a factor (we can't "make more oil", we can't ignore patents, and economies of scale can not be duplicated). On the last point, what I'm saying if production cost per unit have an inverse relationship with sales volume, than bigger companies will have an advantage that smaller do not. Or put another way, we can't have 50 mass makers of computer processors with the same scale benefits AMD and Intel enjoy now.