yes there is - make a worgen class trial and try it out. it’s both a sound and an animation. It’s about as cool / not cool as the Tauren one and it’s an Alliance-only emote. Exactly what you asked for
Technically, Horde only has a custom emote with a sound.
Alliance has a custom emote with a sound AND an animtation.
Alliance has a more advanced custom emote than Horde
Miscellaneous
Tauren are the only race that produce the proper sound effect when the “/moo” emote is used.
Worgen are the only race that produce the proper sound effect and animation when the “/sniff” emote is used.
What I need to say though, is that Blood Elves have by far the cutest /cheer