Ubunto 12.04, is the lowest possible version that will run unity games. The + means anything above that version should also run Unity based games. So it should run in the latest version of Ubunto. And if it runs on Ubunto (and other devs aren't having issues either)... it should run on Ubunto.
Paizuri does appear to be a basic visual novel, but under the hood it's capable doing a lot more then most VN systems out there. For one, we can do fully in-game animated H-Scenes (they're not rendered videos btw) which leads to smaller build sizes. It was also built with WebGL and scalability in mind. So if we wanted to do something that was in full 3D with VN style dialogue, we can.
Ren'py has it's limits. Try doing something in 3D for one. It also can't do a lot of things we want to do, like certain visual effects, WebGL or fully animated H-Scenes (that aren't a 200mb+ video file). It also isn't very scalable beyond a VN style game, at least not without a battle.
I've heard great things about Godot, but code can never be done as a straight copy or import. You would have to migrate your code base which means re-doing everything, so that your code can actually leverage everything Godot has to offer. IF we were ever going to use it, I'd use it for a new project and build from the ground up, learn it properly, and make use of what it has, and optimally. Migrating a whole project to an engine you know nothing about is not something you do lightly.
So with all that said... I'm looking into a VM to run Ubunto. So if it runs in Ubunto... it runs in Ubunto. But if you (or anyone else) run it on Ubunto, and have issues. Let us know.