Is it possible for teeth to recover from neglect through simple daily care?

Probably not: Other than gingivitis, problems like cavities, gum disease, missing teeth, and broken fillings all need to addressed by a dentist. Simple routine care is just that.. Teeth don't magically regenerate because you are brushing them.

Dental Health: Recover from what? Slight gum inflammation can resolve with better oral hygiene. Very early enamel decalcification can recover with proper oral hygiene and remineralizing toothpastes. Almost everything else requires proper dental treatment. Regardless of your situation, see a dentist for an evaluation, proper care, and then start fresh to a life of good dental (and therefore medical) well-being.