Is it actually true that an mri of the neck will detect esophageal cancer?

Unlikely: There are some lesions in the pharynx and high esophagus that might be detected by neck level studies most are by esophagoscope, swallow x-rays, ct scans.

See answer: The majority of the esophagus is in the chest, not the neck. Depending on the field of view, the esophagus may not be included in the scanned territory. The best way to assess esophageal carcinoma is with endoscopy, not MRI – talk to your gastroenterologist.