Again, the Tier 2 team confirms that the scripting works. However, Wordpress.org can have issues with Javascript, and this is something I'll be alerting our Knowledge Base team to so they can make sure our articles are updated accordingly.
Tier 2 is referencing this article on WP, regarding adding javascript to the site to (potentially) allow the archive to work. Beyond that, there's no other insight we're able to provide in regards to making the archive widget work on your client's site.
If your client ends up needing a workaround for making their emails accessible on their website, they can grab emails' individual share URLs, and add those to their website (or have you do it) as desired.
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