Whether or not a character gets accepted to the game depends mostly on the application that is submitted rather than the amount of canon that is available. For example, we have accepted characters like Uchiha Izuna (Naruto), Lily Potter (Harry Potter) and Regulus Black (Harry Potter) before even though they have had very little 'screentime' so to say. These characters were accepted because the muns did a good job of analyzing those characters, drawing reasonable inferences and conclusions as to their personality and motivations from what's seen in canon rather than relying on pure headcanon.

In other words, so long as your app for her is more of a reasonable analysis of Eri rather than summary of your headcanon, there's no reason why you shouldn't try apping her!