Possible to display shortcode based on the category?

Everything’s possible, if you take the right approach.

What I’ve interpreted from your question is, that you want an specific shortcode to be added to your content when the post is in a special category. What you can do is to hook into the_content filter and add a shortcode, if the post is in a particular category.

add_filter( 'the_content', 'wpse314950_add_shortcode' );
function wpse314950_add_shortcode( $content ){
    global $post;

    // Check if this particular post has that category
    if ( has_category( 'my_category', $post ) ) {
        $content .= do_shortcode( '[some-shortcode arg_1="123" arg_2="xyz"]' );
    }

}

There might also be more approaches, such as:

1. Adding a shortcode in the content automatically (using JS or jQuery)
   when the author chooses a category
2. Adding the shortcode to every post and then stripping it out on other categories