«Is that possible?»

Have you tried it? But I think it works - the code is practically like the example from the Plack Handbook page 22ff. From ibidem:

Just like other middleware, using Auth::Basic middleware is quite simple:

use Plack::Builder;

my $app = sub { ... };

builder {
    enable "Auth::Basic", authenticator => sub {
        my($username, $password) = @_;
        return $username eq 'admin' && $password eq 'foobar';
    };
    $app;
};
[download]

This adds a basic authentication to your application $app, and the user admin can sign in with the password foobar and nobody else. The successful signed-in user gets REMOTE_USER set in PSGI $env hash so it can be used in the applications and is logged using the standard AccessLog middleware.