I'm not sure about that. Unlike GMO crops, you (probably) can't patent the dodo… so after a company spends a large amount of money upfront on genetic engineering, as soon as the first batch of birds goes out, anyone can start breeding them and undercut them on price.
Maybe they could find something in their specific breed of not-actually-a-dodo that's patentable.
Or they could only distribute one sex of bird to the public, at least initially.