Where would you use this? At first I thought you meant the party screen (accessible from the pause menu and during battle and so forth), but then you mentioned the "box menu" (which I presume you meant as the party screen) to be something different.
Your idea is an odd shape, by which I mean it wouldn't fit into the standard screen resolution of 512x384.
To strictly answer your question, it's feasible. All it would be is displaying a certain picture (sprite) depending on the species of the Pokémon, which is what all Pokémon icons and battle sprites already do, which is easy. Well, easy enough, anyway. The real question is what else you want to do, which matters in both a technical and aesthetic sense.