Lets assume you are using TCP. When you call send, the data that you are sending is immediately placed on the outgoing queue and send then completes successfully. If however, send is unable to place the data on the outgoing queue, send will return with an error.
Since Tcp is a guaranteed delivery protocol, the data on the outgoing queue can only be removed once acknowledgement has been received by the remote end. This is because the data may need to be resent if no ack has been received in time.
If the remote end is sluggish, the outgoing queue will fill up with data and send will then block until there is space to place the new data on the outgoing queue.
The connection can however fail is such a way that there is no way any further data can be sent. Although once a TCP connection has been closed, any further sends will result in an error, the user has no way of knowing how much data did actually make it to the other side. (I know of no way of retrieving TCP bookkeeping from a socket to the user application). Therefore, if confirmation of receipt of data is required, you should probably implement this on application level.
For UDP, I think it goes without saying that some way of reporting what has or has not been received is a must.