Saving Date Changes to Online Stored images

Hi

I have a question about date change. 
I am scanning old pictures that I import into the Lightroom cloud using Lightroom mobile. 
I then modify the date on my PC. 
Using Lightroom Classic, there is an option to save this modified metadata into the files themselves that are local. 
But the original files are on the cloud. 

Are these files updated? Or is the modified metadata only saved to the online catalog?

Thank You