This would be such a popular feature that I'm surprised Sharkey doesn't have it.
It absolutely shouldn't, it would increase @puniko@mk.absturztau.be 's server costs exponentially as everyone uses her extensive collection. But I'm surprised something being a bad idea would stop the devs.
If you could reference custom emoji on a different server. Being able to invoke custom emoji with :neopuniko@mk.absturzt.de: would lead to everyone pointing at you instead of making local copies.