At the moment, not so far as I know. The challenge for any client is that Mastodon (right now) doesn't load entire threads unless you're on the same server as OP. Instead, the API object says the post is "in reply to this post." If no one on your server is following the post directly prior to that in the thread, then the chain is broken.
There's a bot called FediFetcher that an admin can install to pull in other toots in a thread. Vanilla Mastodon is already working on an effort to integrate this functionality directly but I don't know how soon it will be live.
There's a browser plugin called Substitoot that will pull in other parts of a thread provided you click on the next post up in the thread (in my experience this may take a few clicks).
Lastly, I hear that GoToSocial already pulls in the rest of the thread.
None of that does exactly what you asked for but it's a prerequisite to implementing what you're hoping for.