As far as I am aware, there is an exchange of 'success' (or otherwise) at the end of a fax transmission.
There is, actually at the end of each page.
The process starts with the sender dialling, the receiver answering, and the modems training (at this point, the modems will select the fastest speed they can both do) - the screech sometimes heard before the machines turn the speaker off. The two ends then exchange information on capabilities and what's desired - and agree the transmission scheme to be used. Along the line, the machines also exchange identity - the number (often incorrect) that gets reported on the printouts and reports.
Then the sender sends a start of page message, followed by the page data, and an end of page message. The receiver acknowledges each end of page and the sender carries on. There is no error detection or correction as standard, I can't recall if it's optional.
After the last page, there's a final handshake.
In terms of immediacy, many (most ?) machines these days will scan the document into memory and only then start sending. Some start sending as soon as they've got a page scanned, but most I've used scan the whole thing first. Older machines had a very limited memory, and so would "scan while they send". To know if it's been sent you need to refer to the machine logs, or trust that it'll print a failure page if it didn't go - or specifically set the machine to real-time mode.