Curious if this is appropriate for resizing, alpha transparency, etc.
All blur and glow effects are raster, even in Illustrator. The difference with Illustrator is the Document Raster Effects Settings (DRES) in the
What the DRES items does is tell Illustrator what ppi to rasterize the effect at.
While working in AI, the DRES setting controls the pixel density of the blur/glow. Higher DRES settings result in smoother soft transitions. When objects with blurs/glows are transformed within AI, the raster effect is recalculated on-the-fly and a new raster image for the effect is created. Since this is all done "under the hood" so to speak, it may appear as though blurs and glows are no different than other objects, but they are very different than vector objects. They are always raster objects. They are merely redrawn when needed while you work on the file.
Upon output or export or saving to a flat file format (eps), the DRES setting embeds a raster image of the blur/glow at the DRES PPI setting. So, again, it's a raster image and bound by all traditional raster restrictions.
So, in short, no. Blurs and glows are always raster images and are never vector. Illustrator merely handles these internally-created raster image a bit differently than you may be accustomed to.
Actually the gaussian blur was never vector to begin with. It is just rasterized on fly to your document raster settings. If you resitze or modify the underlying object it just gets rerasterized.
So while inside illustrator the gaussian blur acts as if it was vector. And it might not be wrong to say it is vector, if you think about on screen rasterisation. But if you zoom in on it you will see that it is in fact pixelated.
So whenever you move out of illustrator it will definitely be raster. But then its just a question of when it is rasterized. E Most graphics get rasterized at some point.
UPD-edit: No, the gaussian blur effect is not vector. I was completely wrong thinking that it was. (And writing it here some time ago)
As Scott wrote above, this Blur is just recalculated each time object is being changed in any way. The blur value doesn't change with a plain transformation of an object (even though "Scale Strokes & Effects" is checked in a Transform panel).