Provided that each .pl file has permission to be executed, you can easily achieve your purpose by using something like this:

#!/bin/sh
# stop on first non-zero exit status
set -e

1-search_user.pl
2-prepare_2update_user.pl
3-backup.pl
4-run_update.pl
[download]

Update: This could be a Perl version if each .pl returns a true value:

#!/usr/bin/perl
do '1-search_user.pl'
and do '2-prepare_2update_user.pl'
and do '3-backup.pl'
and do '4-run_update.pl'
or die "error occurred\n";
[download]

I found the sh version much simpler.