Yes, Phoenix is great for applications where you want to use a persistent, two-way connection between server and client, where both the client and the server can keep sending updates to each other without needing to reconnect each time. This is what indeed enables ‘real time’ applications.

When building things like a chat application, each time someone posts a message, Phoenix will forward this message to all other open connections (that are part of the given context, i.e. chat room). The database is no part of this.

Because connections are persistent, Phoenix does not need to look at the database when a new request comes in. Instead, the database is only used to log what happened, so someone that connects at a later moment is able to see what took place.

So, because all of this is happening in memory, with the database being only an observer of the changes that happen, this kind of communication is ridiculously fast. What sort of delay you can expect is of course highly dependent on the needs of your specific application, but you might like to take a look at this benchmark, which shows that Phoenix can handle two million persistent connections on a single server with a non-trivial application without a problem.