Most conspiracy theories follow a few rules:
1) They are based on seemingly imagined Data.
2) They seem to lack tangible, or verifiable fact.
3) They require ever more creative interpretation as they are examined.
4) They are of an incredulous nature from the onset.
5) Those that believe them are not swayed by logical argument.
6) They are generally meant to question or refute established fact.
Given these criteria, does the story of creation fall under the label of Conspiracy Theory?
No, I don't think that creation stories are conspiracy. They are stories, they serve a cultural purpose, mainly a beginning of the world, they are never inspired by fact, but inspired by spirituality. Which is why I really see no conflict between the Bible and science.
That being said many people who take folklore as fact and deny all evidence that says that folklore is not fact are similar to conspiracy theorists.
Every culture told tales of the origins of the earth, or the species, some are fantastic fiction, others are similar to the generally accepted academic account.
We are a culture that is entertained by fiction, novels, TV, video games, they may not be factual in their fabrication but their value shouldn't be measured on their accuracy. Story telling has been part of humanity for eons, where the occurrence the stories are told about may not have happened exactly a they are described, the value is not in the events but perhaps in the plot. One such fable comes to mind, the grasshopper and the ant, there was a purpose to that story, it wasn't that grasshoppers and ants compare in their ability to plan for the future.
Just like the plot of the various origin stories.
Honestly who cares that people believe things like Genesis actually occurred, what harm does it cause? It absolutely has not encumbered the advancement in the understanding of science such as evolution, frankly it has been a quite modern that we do have a fact based scientific notion of the origin of the universe, planets, and life. If I am not mistaken Charles Darwin was the first to formulate the origin of the species based on fossil records.
In most origin fables the basics are true, if you omit all the details and things which are metaphor, they all say the same thing, once there was nothing, now there us something, this is a truth that the big bang theory, evolution, coalescence, and any other beginning agrees with, so no, I don't think it can be called a conspiracy theory, a story, fable, folklore, legend, myth perhaps, but a conspiracy, to what end?