I haven't tried dry ice in kitchen equipment, but have destroyed a plastic measuring jug with liquid nitrogen (the scale had become illegible so I took it into work where it would be handy, then abused it). The failure mode could be expected to be relevant to plastic and glass used with dry ice.
Many plastics become brittle at low temperatures - this can even be seen when using some plastic food storage boxes in a domestic freezer. Cooling also causes thermal contraction, and most of this will happen by the time you get down to dry ice temperatures. Because of the low thermal conductivity of plastics (and glass) the inside shrinks but the outside doesn't because it doesn't cool much. In the case of my jug, the strengthening/supporting ring on the bottom stayed at room temperature when the rest cooled, and the bottom dropped clean out of it. While dry ice is far warmer than LN, it's still cold enough for embrittlement and a lot of thermal contraction.
That's not to say it will fail, only that it might. Dry ice doesn't make such good contact with the container as LN, but localised cracking could still be an issue with plastic parts. A glass jug would likely fail completely even with localised thermal cracking. Borosilicate (some Pyrex, either old or European - I don;t know if it's used in blenders but it's possible for ones that are mean to take heat) or metal should be fine (careful handling the metal).
I'd research the cost of a replacement part, but probably risk it, taking a few steps to reduce the risk:
- precool if possible, in a freezer (for even contraction; this will also reduce the amount of dry ice you lose)
- add the other ingredients first if possible (though you sound like your recipe breaks it up before mixing it in). When making LN ice cream, drizzling it into the ingredients while stirring is the usual method (this is me holding the bowl while one person stirs and another pours).
- add the dry ice through a feeder cap if your blender has one (mine does) with it running
Many blenders use polycarbonate jugs. This is a tough plastic that can handle hot liquids, so is a good choice if you're putting soup in there.
I had an offcut of polycarbonate (Lexan) at home, and while I don't have access to dry ice, I can get liquid nitrogen, which gets even colder. The first thing I tried was cooling a piece of aluminium to -100°C (a little cooler than dry ice) and resting it on the polycarbonate for a few minutes. There was no cracking . Even immersing the polycarbonate in liquid nitrogen for several minutes didn't make it brittle. So a polycarbonate jug (not all plastic blender jugs are polycarbonate, but many are) should be absolutely fine with dry ice.
Applicability to glass
The specific model in question here uses a glass jug. I can't find anything definitive on the type of glass. If it's borosilicate (as suggested by some branding, according to a review, but I'd be very wary of sharing that assumption) I'd expect it to be fine. If it's normal soda-lime glass, there's a small risk it could fail suddenly.