Can websocket messages arrive out-of-order?

If we send two messages over the same html5 websocket a split millisecond apart from each other,

Is it theoretically possible for the messages to arrive in a different order than they were sent?

Short answer: No.

Long answer:

WebSocket runs over TCP, so on that level @EJP 's answer applies. WebSocket can be "intercepted" by intermediaries (like WS proxies): those are allowed to reorder WebSocket control frames (i.e. WS pings/pongs), but not message frames when no WebSocket extension is in place. If there is a neogiated extension in place that in principle allows reordering, then an intermediary may only do so if it understands the extension and the reordering rules that apply.

It's not possible for them to arrive in your application out of order. Anything can happen on the network, but TCP will only present you the bytes in the order they were sent.