This is possible to do. You just need to know a very rarely used feature*.
- First turn on transparency grid, so that you can observe the effect. Choose: View → Show Transparency Grid or hit Shift + Ctrl + D.
- Next make a primitive shape like a box to design the effect on (due to text grouping it is easier to design on something else first).
- In the appearance window Select the entire object (usually Path topmost item)
- In the transparency window click on knockout group 2 times so its a check mark (If you can not see options in the panel menu enable extra options).
- Duplicate the fill color
- Offset the shadow using transform effect.
- Add a white stroke
- Magic step, turn opacity of stroke to 0 and it will cut trough the shape because you are using group knockouts.
Image 1: You should have something like this.
Now drag this shape to the styles panel and apply to your text.
Image 2: Final result after some changes in stroke thickness and transform amount.
* In fact it is so rare that whenever I even suggest this to people I get blank stares followed by why would I need this?