The internal byte counter that sums up up volume for quotas only sums the bytes_to_client. This is internally written into the quota module and can't be altered. I don't think you are going to be able to do this with outbound bytes.
In general, when a quota session expires, it does not terminate existing connections. A GET or POST that is in progress should not be terminated. It will deny subsequent requests after limit is reached.
That said, not all transfers consist of a single GET or POST.
For example, if you watch a 45 minute video and your quota is 30 minutes for the day, in theory you should be able to sustain the viewing of the video. But the entire viewing process is not just one long GET. It's a series of small GETs that bring in buffered segments and plays, then GET the next segment and play. So if the timer expires, you will be unable to request the subsequent segments.