Your premium will be based on the entire item's value, not just the diamond. Sometimes this difference is tiny, sometimes it's important. It depends on what you have. Replacement values are routinely more than discount transaction costs but double is usually a bit much and raising the value declaration above the cost to actually replace doesn't do anything other than raise your premiums. If YOU can replace it for $xxx, chances are good that they can too.
The company's behavior in the case of a loss is going to be based on the description and the photographs provided in the appraisal, not the value conclusion.