Depending on where you live, your deductible may be higher under certain circumstances. For example, in Florida, your deductible for hurricane damage is much higher than if your home was burglarized. So, will your insurance company pay or won't they? Look at it this way, insurance companies DON'T want to pay. They are in business to generate profits and will need to be convinced BY YOU that the claim should be paid. The burden of proof lies on you, the homeowner. This means that you will need to prove your case and do it well. The better prepared and more organized you are, the better.
Start with documentation. You may need to take dozens of photos and provide your insurance agent with detailed estimates to counter against the insurance company's original settlement offer. You may need to demand to see how the agent depreciated your property and negotiate a more reasonable method. While your homeowner's insurance policy is a contract, the claims process does provide room for negotiations with auto insurance company (more information on best negotiation tactics in How to Contact with Auto Insurance Company? article).
Arm yourself with knowledge, documentation, and real-world estimates while also considering professional representation and you'll be better equipped to answer the question, "Will they pay for it?"