Is it appropriate to use emoji or similar icons in a paper?
I'll answer from the perspective of a different field. In the biomedical sciences, it isn't uncommon to use some cartoonish representations to depict animal tasks/procedures, particularly because actual pictures of animal subjects are often avoided for a number of reasons. The same can be true for human subjects.

I wouldn't think twice about seeing a smiling versus frowning monkey indicating task performance in a figure, as long as it was instructive/guiding and not interrupting/distracting. Same for other types of icons like thumbs up/down. Certainly emojis in text would be totally different.