Is it possible to hide or move default macOS apps?
Which applications are you having trouble moving? I tried a few: Photo Booth, Calendar and System Preferences.  They all moved to the new location without any issues, and also functioned after the move. 



You can hide files fairly easily in the Terminal.app:

sudo chflags hidden "/Applications/Chess.app"


to unhide:

sudo chflags nohidden "/Applications/Chess.app"



You'll need to enter admin password after entering either one of these commands 
You can drag a file to the Terminal window to get the file path. It doesn't add the double quotes around the file path, but that should not be necessary in this case. If it doesn't appear to be working, you may wanna try adding the double quotes.




You don't need to see the file to unhide it, but it does help so you can easily copy the path and you don't need to remember which files are hidden. Seeing hidden files in Finder is a little less intuitive though...

If you want to see all hidden files in the system, there are applications where this is a built in feature: TotalFinder, XtraFinder, Path Finder, Commander One...but you can show them in Finder as well, using the Terminal.app:

Should be noted that both of these commands here will close all finder windows

defaults write com.apple.finder AppleShowAllFiles YES; killall -KILL Finder


And to hide all hidden files:

defaults write com.apple.finder AppleShowAllFiles NO; killall -KILL Finder