Yes. SSEs are just an infinite-length HTTP body formatted in a particular way. And like all HTTP bodies, they are guaranteed to arrive in the same order the bytes were sent.
Server-to-client, yes. The moment you write a little chat app that sends every line you type as separate POSTs -- which can be reordered -- you get to keep both pieces.
I wish browsers would support streaming request bodies in the fetch API. That would obsolete WebSockets practically immediately.