Constant MC - Monopolstic Competition
It is possible for firms to have constant marginal costs in monopolistic competition in theory. Nevertheless, they must also have fixed costs. The fixed costs prevent firms from entering in sufficient numbers such that you would have perfect competition. 

As to whether constant marginal costs are realistic in you scenario, that depends on what you believe about the industry in practice. That would require detailed knowledge and expertise of this specific industry, which you are unlikely to find on this site.

Note, however, that just because the company has already bought the materials does not neessarily mean that these costs do not matter. For example, the company may still want to use less material per production output, because it could resell the unused materials. So the company in that case still cares about the costs associated with the use of each unit of material.

It is a bit unclear in your example what this company actually produces. However, if you think the costs of producing one extra unit are the same, regardless of how many units you have already produced, then you are justified in assuming constant marginal costs.