No, only raster images are supported (PNG or JPEG). While Spine is useful for all kinds of animating, it has games in mind and very few (none?) game toolkits support rendering vector graphics. The reason is that it's quite hard and performance isn't good.

I, for one, would love to get this puppy working with spine: https://www.assetstore.unity3d.com/en/#!/content/38258 - think about it, both systems work with a mesh target, but said mesh would get filled at runtime with the optimal graphics for that screen.

Currently, with the png's, I'm having trouble getting my aliasing right because I'm unsure what scale of assets to use. This (SVG's), in my mind, could perhaps solve that issue?

Spine's runtime rendering is separate from its data model. You could animate a Spine skeleton and then use the bones to transform SVG meshes instead of texture regions.

You can animate in Spine at one resolution and use a different resolution at runtime. Not sure what you mean by aliasing. In skeletal animation texels are almost never aligned with screen pixels, so there will always be filtering. It's not normally an issue because everything is moving, since that is the point of animating after all.

I would find it useful to be able to use svg's in Spine, whether it's for rendering the vectors at runtime with that Unity plugin or just to allow you to export from Spine at any resolution.