What happens if the database node's network fails just after commit and before responding to the client
The simple answer is, that a transaction is committed after responding to the client. And it's the client that's sending the commit, the server doesn't decide on its own, when a transaction is finished. (I'm having a hard time finding reliable sources for this, I must admit, but you have my word. It makes sense)  

I tested something similar after it wasn't clear to me when a statement is written to the slow-query-log (the manual isn't clear about this). For this I throtteled my network bandwidth in Linux with netem. The result was, that the statement duration in the slow-query-log includes the time until the result is transmitted to the client.
Feel free to do a similar test :)