Does the template engine have a view built-in for archive pages for custom metadata, like it does for tags?
Yes. Let's say you've set the custom metadata Apple, like so in some of your posts:
Apple: yes
You can list all posts with Apple metadata set using the following in your template:
{{#all_entries}}
{{#metadata.apple}}
<a href="{{{url}}}">{{title}}</a>
{{/metadata.apple}}
{{/all_entries}}