When I say "If a CDN is critical to your site's performance you should put your site on it" I do mean to say "put (those parts of) your site on it" not "if 51% of your site should be on a CDN put the other 49% as well".
But to your question though even un-cacheable content can be "those parts of". There are products from CDNs like https://blog.cloudflare.com/argo/ which combine CDN cache tiering with higher tier network transport to origin servers for all cache misses (or uncacheable content). Again though, it depends on if it's critical to your site's performance or not. If you don't have a bunch of uncacheable content, that content doesn't need the absolute best transport, or the time/money could improve some other part of the site speed more then it's not critical to your site's performance.
But to your question though even un-cacheable content can be "those parts of". There are products from CDNs like https://blog.cloudflare.com/argo/ which combine CDN cache tiering with higher tier network transport to origin servers for all cache misses (or uncacheable content). Again though, it depends on if it's critical to your site's performance or not. If you don't have a bunch of uncacheable content, that content doesn't need the absolute best transport, or the time/money could improve some other part of the site speed more then it's not critical to your site's performance.