Illustrator sort of has this feature, it's limited but, can do what you ask. In fact this is one of those features that they have made worse in CC by disabling symbols within symbols, which in this kind of design case could be useful*. So be warned your mileage varies depending on what version of Illustrator you use, newer not equating better here.
- Create a logo in black on paper.
- Make it a symbol.
- Drag symbol on a black background (nothing visible yet).
- Make the symbol 100% transparent.
- Group symbol and background.
- Turn the Knockout Group on for the group in the transparency panel extended options (if its not visible enable options form the menu call out of transparency window). See this post for more info.
The logo should now cut trough the black background. To edit the logo double click on any instance edit then exit isolation mode and both should update.
Image 1: Symbol shared in different settings.
This is just one way it is possible to use styles to color symbol instances for example. In this case it may be a good idea to make the logo without colors at all as it makes easier to apply styles.
Image 2: Same symbol with ugly effects applied. Image is still live editing any of the symbols changes them all.
* Imagine logo text on right, below and in different colors, logo cuts into square but is only partial etc etc. :)