Air conditioning was a wonderful invention, that’s for sure. Whether home insurance will cover your AC unit depends on what caused the damage.
In your case, it seems like the AC needs to be replaced due to normal wear and tear, which will not be covered by your insurer. Damage to objects due to negligence, normal aging, or avoidable causes (like a rat infestation) will never be covered by homeowners insurance.
Additionally, the type of coverage for your AC unit depends on whether it is a central or a window unit. Window units are covered as house contents, while central units are structural elements of the house.