Basically, the battery has a lithium (Li), sodium (Na), or potassium (K) metallic anode, a solid glass electrolyte, and an "ink" cathode of sulfur (S8), ferrocene (Fe(C5H5)), or manganese oxide (MnO2) on a copper (Cu) current collector.
So it's not entirely solid. The cathode may have a tiny bit of liquid electrolyte between the glass and the copper.
I would guess that microfractures in the glass would impede the movement of charge carriers, even if it didn't shatter outright.
It wouldn't be good for the battery to hit it with a hammer, I think, but that really applies to any high-energy-density battery. Not all glasses are created equal, either. It all depends on the composition and the cooling regime. Some glasses can shrug off small-caliber bullets, and others will crumble under your fingertips.
So it's not entirely solid. The cathode may have a tiny bit of liquid electrolyte between the glass and the copper.
View a helpful diagram at http://www.greencarcongress.com/2016/12/20161213-braga.html .