No it doesn't support that, but systemd-socket-proxyd does. So my Systemd service exec line looks like this:

ExecStart = /path/to/systemd/lib/systemd/systemd-socket-proxyd --exit-idle-time=20min /path/to/jellyfin.socket;

https://github.com/attilaolah/dotfiles/blob/144d1711755d7a9e...