Googlebot and other spiders can process some JavaScript, though it is true that having the content you want indexed in the underlying HTML is always best.
One way to verify whether Easycomment's content is indexed is to look for other sites that have Easycomment installed, then do a site:example.com search for those sites. You can even test on your own site if you don't know of others using it. Add a few seed comments, submit your sitemap or page through Google Search Console, later verify that it's been indexed by searching for that specific URL, and then search for something like "site:example.com wording in your comments" (replace the URL with your site, and replace "wording in your comments" with something you actually typed in your comments). If you know the page has been indexed, you can then tell whether it's indexed the comments by searching for unique content only found in the comments.