Although i am quite sure this is possible (see Template::Provider) you probably do not want output these comments in your production environment as you will give clues away to any would-be attackers. Instead, why not just grep or ack for the markup in question? I have found this to be a very workable solution for tracking down templates. No need to add more code to your base.

UPDATE: this might work for you, but i still recommend using grep or ack:

use strict;      
use warnings;                
use Data::Dumper;            
use Template;                

my $file = 'src/greeting.html';
my $vars = { message  => "Hello World\n" };

my $tt = Template->new;
$tt->process($file, $vars);

my ($found) = keys %{ $tt->{SERVICE}{CONTEXT}{LOAD_TEMPLATES}[0]->{LOO
+KUP} };
print "$found\n";
[download]

L-LL-L--L-LL-L--L-LL-L--
-R--R-RR-R--R-RR-R--R-RR
B--B--B--B--B--B--B--B--
H---H---H---H---H---H---
(the triplet paradiddle with high-hat)