Unfortunately no, that is only for installation via windows. There is no Linux updater for it. Still no stable update on Linux for the 12th gen :(
Edit: oh nice actually I see they added an EFI updater! That’s great progress :) so I stand corrected – 3 years after launch, it got its first and only stable update on linux! Thanks for the correction.
Correct they do not, there are components on some models (like the 12th gen) that they do not support updating using fwupd. You must use either EFI updater or update from windows to get the full update on those platforms.