Not quite. The not not transformation maps 0 to false and every other integer to 1. False acts as the nul string in string context, and acts as zero in numerical context.

use warnings;

my $false   = !!0;
my $numzero = 0;
my $strzero = '0';
my $nulstr  = '';

local $\ = "\n";

print 'false: ', $false;      # ''  <-- Not zero!
print '0:     ', $numzero;    # '0'
print "'0':   ", $strzero;    # '0'
print "'':    ", $nulstr;     # ''

print '';

print 'false: ', 0+$false;    # '0' (no warning)
print '0:     ', 0+$numzero;  # '0' (no warning)
print "'0':   ", 0+$strzero;  # '0' (no warning)
print "'':    ", 0+$nulstr;   # '0' with warning
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If you wanted something that maps 0 to 0 and every other integer to 1, you'd want 0 + !!$var.

Update: Added $strzero. Minor cosmetic changes.