Can acid reflux cause esophageal cancer without ever having barretts esophagus?

Yes and no. Acid reflux is not clearly a cause of esophageal cancer. But there is an association of reflux (acid and non-acid) to barrett's esophagus/adenocarcinoma of the esophagus. There are other types of esophageal cancers, which may or may not be related to reflux.
Let me explain. A particular enzyme is significantly higher in cancer cells that have been exposed to acid, leading to the overproduction of hydrogen peroxide, and offering a possible explanation for how acid reflux may lead to cancer of the esophagus, according to a recent study in the journal of biological chemistry.