turning it on for the script will turn it on for everything including every module that is used by the script. Is that correct?

Correct. eg:

$ cat ptt.pl 
use strict;
use warnings;
use Path::Tiny;

path ($ARGV[0])->spew (@ARGV);
$ perl -T ptt.pl foo
Insecure dependency in sysopen while running with -T switch at /usr/sh
+are/perl5/vendor_perl/Path/Tiny.pm line 830.
$
[download]

It would be of rather limited use otherwise.