I doubt it. Insurance is usually either at indemnity (depreciated value) or reinstatement/replacement value (What is market value?) neither of which will see a payout more than the insured/at risk/agreed value. A global loss adjuster like McLarens is engaged by the underwriters to make sure there is no 'betterment' or fraud.
if you're under insured or within 90% of the insured value, look forward to the term 'average', if you're 'over insured' it's not really a win either as you have been paying a proportionate premium against the insured value/asset since you put it on your schedule