In general I guess you can say that server-rendered websites are easier to assume they are archivable, but that doesn't mean a bit of client-side scripting will break the archiving process. If the scripts are also fetched (and not relying on 3rd party domains), the fetching and rendering process should work the same as long as the UI doesn't depend on API responses. Lightweight scripting, especially done within the <script> tags of the page, will work perfectly fine for most archiving software. Keep in mind all of them already fetch data from <img> tags, and most fetch 1st origin <script> src's as well.