See Mojolicious Guides Testing: The Test::Mojo-object.

In short, yes, you can specify the entire URL to issue requests against, allowing you to test remote web applications. This works because Test::Mojo contains a Mojo::UserAgent object.

As an example:

#!/usr/bin/env perl

use strict;
use warnings;

use Test::More;
use Test::Mojo;

my $t = Test::Mojo->new;
$t->get_ok('https://www.perlmonks.org')
  ->status_is(200);

done_testing();
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If you run that you should see:

ok 1 - GET https://www.perlmonks.org
ok 2 - 200 OK
1..2
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