No, that's exactly how it works. Why would you write such a thing when you're clearly just guessing?
A shell script is interpreted one line at the time.
Very simple proof:
$ while true; do printf 'date\n' && sleep 5; done | sh
Mon 16 May 2022 07:19:21 AM CEST
Mon 16 May 2022 07:19:26 AM CEST
Mon 16 May 2022 07:19:31 AM CEST
In either case, if the network connection is interrupted, the download is finished. How would sh know it's not the whole script as the author intended it? Remember that in a pipeline the receiving end only sees the pipe, and won't know about the exit status of the process upstream (which may for all we know be zero anyway).
I find it hard to believe you could interpret a partial script on the fly as more comes in via stdin.