It is an option, however I don’t think it will change the results dramatically because, again, all the emojis in this particular dataset are not really that different even if you do filter them a bit (it’s still going to remain positive, basically). For example, what exactly distinguishes several different kinds of heart emojis? What I mean is that keeping, let’s say, only a smiley, a heart and a tree won’t really make it more interesting, unfortunately. There’s not even a sad emoji 
Meanwhile, the DeepEmoji demo definitely offers a much larger range of emojis. I can’t figure out what data it was trained on though. It would be nice to use it.
I was thinking about maybe doing sort of augmentation by means of replacing emotion tags with emojis in the same dataset in combination with the aforementioned filtering. It’s not an exact solution, but it should be okay for a fun project.