Does Geosgaeno ever drop four-slotted weapons?

[Tavrobel]

lol, well what I'm trying to achieve is getting a four-slotted weapon which actually includes No Encounters, because normally you can't Customize that ability to a weapon.

Why would you do that? It sort of defeats the purpose of having a weapon in the first place. I've also not seen Geosageno ever drop an armor with four total slots, so it's not very likely that you would get one.