Since a properly created package has a MANIFEST file, you could extract just that, then use Module::Locate to test if the modules in the package have been installed.

Disclaimer: Not tested. YMMV

#!perl
use strict;
use warnings;

use Archive::Tar;
use Module::Locate qw/ locate /;

my $tar = Archive::Tar->new;
$tar->read('origin.tgz', COMPRESS_GZIP, {filter => 'MANIFEST'});
my @files = split /[\r\n]/, $tar->get_content( 'MANIFEST' );
my @modfiles = grep s|lib/||, @files;
my @modules = map s|/|::|, @modfiles;

for (@modules)
{
    my $p = locate($_);
    if ($p)
    {
        print "Found '$_' at '$p'\n";
    }
    else
    {
        print "Not installed: '$_'\n";
    }
}
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