Using emoji is basically making reference to a data object stored in a library on a device, be it smartphone, laptop, etc. These libraries are created by their respective developers, hence why emoji look different on different devices.

But unless you're actually storing, selling, or distributing the artwork or the libraries that contain them you shouldn't have any problem as you're just telling a device reading your document to `insert-object-XXXX-here`.

This discussion on StackOverflow may provide some further info for you: https://stackoverflow.com/questions/10834811/emoji-copyright#16696512

Another on Quora: https://www.quora.com/Do-all-the-emojis-have-copyright