Yes, definitely, Copywhiz supports compression of data into a .zip file.
Just watch this short video for more clarity:
In the Copywhiz main window, you will find an option "Paste as compressed .zip file". Choose this option to compress all the files into a zip file. You will find the same option "Paste as compressed .zip file" when you right click inside Windows File Explorer and choose Copywhiz -> Paste Special option.