Lack imagination...
1: Maybe Cura doesn't happen to do multiple walls in vase mode, but there's no reason it couldn't. It's not like there is anything about a spiral pattern that prohibits it. It's a perfectly reasonable idea and question, and it's physically perfectly possible.
2: So, moving on, fine, Cura's vase mode can't do it. Perhaps a good-enough next best thing in real-world terms is just set walls to 999?
If your model is solid, then maybe first generate a slightly smaller scale copy, and generate a difference in a cad program where you have the smaller copy subtract from the original copy, so ypu're left with a shell that's however thick you want.
It won't be exactly like a multi-wall vase mode, just mostly. Vase mode would have no vertical seam. Walls=999 would. Or it could have a lot of random points instead of a seam, and with layer change wipe, that might be blended out pretty well. You could probably fake it pretty well with some playing around.