Yes, we support emoji. Type ":" to see a list of suggestions. This list will update as you type more characters; try typing ":b" for example. For more information, you can find a cheat sheet here (be prepared for lots and lots and lots of emoji).
Besides the ones listed in the cheat sheet, we also support the old school short emojis too, like :) for example.
Have fun and see what you can come up with.
Note: Teamwork Chat also supports Markdown.