You'd think so, wouldn't you - but it might depend on the exact wording of the insurance...

Looking at the US Postal Service web site:=
http://new.usps.com/cgi-bin/uspsbv/scripts/content.jsp?D=24915
quotes:

"Coverage is limited to $500 per piece
****(the unit on which postage is paid)****," [my emphasis]
"What happens to the damaged article I give to the Postal Service?
If the article has salvage value, the Postal Service retains it..."

So if you are making a claim for total loss (as I imagine you are given the sum quoted), then you may
 be out of luck.
The same web reference suggests you consult Domestic Mail Manual S010, for more detailed information
 "about domestic indemnity claims".