Would in-office dental fluoride treatments benefit an adult who has both crowns (to protect margins) and natural teeth?

Yes. While most often done on children's teeth, in office Fluoride treatments can help natural teeth of any age remineralize.
Topical Fluoride. Topical Fluoride treatments will help to some extent. The three most important things you can do is brush and floss properly and eat a healthy diet, limiting foods that promote tooth decay and periodontal disease. It's more important for patients who have dry mouths, sensitive teeth and poor oral hygiene as a supplemental way to better dental health.
Fluoride. Yes routine Fluoride rinses especially prior to bed would be helpful. A prescription strength Fluoride with tricalcium phosphate would also be helpful to help remineralize your tooth if a cavity starts. Ask you dentist.