It's one of those thing that sound nice on paper but a actually couple your runtime with ci/cd, if you have anything else beside Erlang what do you do? You now need a second solution to deploy code.
With rolling deployments, your only choice is to wait until that connection drains by completing or failing the download. If that doesn't fit your use case, you're out of options.
If your application is an Erlang app, you could hot code reload an unaffected part of the application while the download finishes. Or, if the part of the application handling the download is an OTP pattern that supports hot code reloading (like a gen_server) you could even make changes to that module and release e.g. speed improvements mid download stream. This is why Erlang shines in applications like telephony, which it was originally designed for.
one of the cool things about unix is (and perhaps windows can do this in the right modes, idk), the running copy of a program is a link to the code on the disk (a link is a reference to the file, without the file name). You can delete a running program from the disk and replace it with a new program, but the running copy will continue and not be aware that you've done that. You don't need to wait till the program finishes anything.
on an every day basis, this is what happens when you run software updates while you are still using your machine, even if your currently active programs get updated. you'll sometimes notice this in a program like Firefox, it will lose its ability to open new tabs; that's because they go out of their way to do that, they wouldn't have to if they wanted to avoid it, just fork existing processes.