CONNECT Will Msg in context of KeepAlive timeout

This is probably a dumb question, but i would like to clarify the following sequence:

Client sends MQTT CONNECT + 'Will' msg, +ve KeepAlive
Server sends MQTT CONNACK
Keep Alive timeout occurs
Server sends MQTT PINGREQ, no response from client.
Server drops TCP connection.

Section 2.2 Will flag specifies 'Sending a Will message is not triggered by the server receiving a DISCONNECT message from the client.'

Section 2.2 Keep Alive timer specifies 'If the server does not receive ... it disconnects the client as if the client had sent a DISCONNECT message.'

Does this mean that if a client fails to respond and the server drops the TCP connection, the Will message is not published?