Below is what I have for discussion.
Wi-Fi is not an issue here, I think. I get into the same situation when I do test QA installs in VirtualBox with disabled network adapter (or disconnected cable).
I agree that both Welcome and Apport should be more user-friendly to warn user that the system is offline. Not sure how and where this should be done.
The discussed Vaio uses Intel Centrino Advanced-N 7260 which should be supported by the kernel drivers. It is good that it is not Broadcom. So wi-fi configuration using network manager should go well.
But in current daily builds we have a new problem - network manager icon (nm-applet) is not shown in tray's indicator area. It is a bug 1955307 (I hope @Wimpy will fix it soon), which maybe temporarily fixed by
sudo mv /usr/lib/x86_64-linux-gnu/ayatana-indicators3/7/libayatana-application.so /usr/lib/ayatana-indicators3/7/libayatana-application.so
sudo mv /usr/lib/x86_64-linux-gnu/systemd/user/ayatana-indicator-application.service /usr/lib/systemd/user/ayatana-indicator-application.service
and reboot.
Then all indicators should be shown in their places. So user clicks on nm-applet, select needed wireless network, enter its password and enjoy.
Then sending telemetry and bug-reporting by apport will be possible.