OnWrite is used when you're using asynchronous IO (when you have ClientType = ctNonBlocking, in other words). It's called when the socket's ready for you to send data.
Thus, your thinking's only half in the desert: if you're using ctBlocking, then don't bother with OnWrite at all. If you need that thread to send data and get on with other stuff at the same time, then use ctNonBlocking and write to the socket in OnWrite.
When you use async sockets, Windows will send your socket a CM_SOCKETMESSAGE, handled by TCustomWinSocket.CMSocketMessage. When that message has its SelectEvent property set to FD_WRITE, the OnWrite's (ultimately) invoked.
The magic ingredient here is the call to WSAAsyncSelect in TCustomWinSocket.DoSetAsyncStyles.