I have created a new emoji plugin for the markdown editor. Initially I created the plugin for myself but after reading this thread I decided to publish the plugin. You can download the JPL file here or you you search for "Markdown Emoji Autocomplete" in the plugins section of the settings.
Feel free to test it out and leave feedback here in this thread.
I'm curious, though, what the use case would be for this over simply using your OS specific emoji picker and putting the emoji itself into the markdown document? I have never understood the need for this kind of feature, but obviously people use it. In Windows I just use Win + ;
It's not possible to insert emojis from the RTE but, emojis are perfectly the same in the RTE (Rich Text Editor) after inserting them in the MDE (MarkDown Editor).