Can WP-Members Membership Plugin be used to hide only a section of a webpage?

Yes; use the [wpmem_logged_in] shortcode described here: https://rocketgeek.com/plugins/wp-members/docs/shortcodes/status-shortcodes/

Does this work outside of the loop in a custom template using do_shortcode in PHP?

Of course, but there are good reasons why you should NOT use do_shortcode() just to call a single shortcode. There are better ways to do it. See this: https://rocketgeek.com/basics/why-you-should-not-use-do_shortcode/

As mentioned in that article, using the direct callback is preferable, and actually, in this case, digging in further, the [wpmem_logged_in] shortcode is really just a wrapper for is_user_logged_in(). So if you’re doing something in PHP, you should just do it as:

if ( is_user_logged_in() ) {
    // ...user is logged in. do stuff here.
}

Thanks so much for your explanation. It is exactly what I am looking for.

I will use your plugin and I am very pleased with your support!
I’ll experiment with it an hopefully I am successful.

-W