You can. explorer.exe may still be running as a process, but visually its presence can be eliminated from the GUI.
Which sounds just like the Finder?
Except I get a new window when I click on the Explorer icon. So no, it's the opposite of Finder's fail-silent behavior.
When I click the Finder icon in my dock, or open it with Alfred, I get a new Finder window. Doesn't appear to be a configurable setting. Not sure what's wrong with your setup.