Short answer: yes.
Longer, somewhat more meaningful explanation: It's incredibly unlikely that what fits into your throat in terms of ice would be wide enough not to melt away enough for later passage… But what if that ice cube is also very long(*)? And what if your throat's internal temperature had already been lowered (let's say you're eating a bunch of ice cubes, outside, in the artic, as your sole means of hydration. In that case, yes, it is certainly possible that you could choke to death from an ice cube… But given all the other mitigating factors at work, I'm not sure I'd credit the cube itself with slaying you.
(* We usually call just about any squared-off three dimensional ice form a "cube", even if all sides are not of equal length)