So suppose I've got a database of behavioral and neuroimaging data from a research study on autism. Is this something that can be used to predict diagnosis from the other data fields?

Yes, I think this would work. For example, you'd organize the data into 3 tables: patients, behaviors and images. The patients table would have a partially filled-out "diagnosis" column. The model would then predict diagnosis of not-yet-diagnosed patients based on the patterns in data fields of previously diagnosed patients.