This is actually quite simple. Unlike keeping the users available for chatting, all you need to do is get them signed in. Therefor you don't need to store the cookies like you normally would enabling you to do multi-logins.

use WWW::Mechanize;
my $mech = WWW::Mechanize->new();

my $url = "url.here";
$mech->get( $url );


   $mech->submit_form(
        form_number => 2,
        fields      => {
            username    => 'name',
            passwrd    => 'pass',
        }
    );

my $mech2 = WWW::Mechanize->new();
$mech2->get( $url );
   $mech2->submit_form(
        form_number => 2,
        fields      => {
            username    => 'name',
            passwrd    => 'pass',
        }
    );

my $mech3 = WWW::Mechanize->new();
$mech3->get( $url );
   $mech3->submit_form(
        form_number => 2,
        fields      => {
            username    => 'name',
            passwrd    => 'pass',
        }
    );

print "done";
[download]

The above code is tested but there are other things to think about, too. You might want to randomly pull a few usernames each time so different users are signed in after each login session. It'll make it look more realistic to people who are looking at account profiles seeing the last access/login time for each user.

You could also add a flatfile database and use a logout script to randomly pull a name or two of your signed in users every X minutes, too.

This is the basics, but think about making it perform a little more realistic.