Is a WebSocket client guaranteed to see messages in the order they were POSTed to the @connections API?

In API Gateway, to push a message to a connected WebSocket client, you're supposed to send a POST request to API Gateway's @connections API.

My question is:

• Will this POST request block until the message has been sent over the network?
• Or, if it returns sooner than that, is it at least guaranteed to be seen by the client before a subsequent POST?

I can't find this guaranteed anywhere in the API Gateway docs, but the usability of AWS API Gateway for WebSocket APIs would seem to hinge on this. If there is no such guarantee, the client could theoretically see messages in a random order.