Will home insurance cover a broken denture?

Highly unlikely. Homeowners insurance is "Hazard Insurance" designed to cover losses to your homes structure or contents, Typical covered perils are Fire, Wind, Hail, Falling Objects, etc.

Dentures and other dental devices are typically covered under your dental policy or program. Unless you could establish that your dentures were damaged by Fire, Wind Hail etc, then there would be no coverage for dentures.