Wouldn't this "secure" that the $start_of_barrel_region is defined?

No, as you can easily verify:

#! /usr/bin/perl
use warnings;
use strict;

my $x;
print defined($x) ? "Defined\n" : "Undefined\n";
print $x;
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my declares a variable, but doesn't make it defined. You have to assign a value to it (other than undef) to make it defined.