What Scott says is true, but since you're talking about the way it's stored within illustrator, there's one thing worth adding.
Within Illustrator, a vector shape with a Photoshop effect applied is stored as a vector shape, plus data about the effect that needs to be applied to it - not as pixels like a rasterised shape or a layer in photoshop. When you alter the vector shape, the photoshop effect is re-applied.
That means that you can scale up the vector shape as much as you like without the pixelation problems you would get scaling up a fully rasterised shape. Here's a simple example:
Both circles pixelate at this zoom level - because as Scott says, it's a raster effect. But both circles pixelate exactly as much as each other, despite the fact one of them has been scaled up. Illustrator takes the settings for the photoshop effect and re-applies them to the newly sized circle. This also causes the effects to look different.
So you might not need to use Live Trace to get what you want - you can 'infinitely expand' the shape, and each time you do, it'll re-apply the effect at the resolution you choose in Document Raster Effects Setting. You can take a tiny image, apply photoshop effects, then scale it up to fill the page and it'll re-apply the effect and will have the exact same level of pixelation as the smaller image.
That said, it might be worth live tracing at some point anyway, to 'fix' the effect. When you scale the image and it re-applies the effect, it might not work in the same way as you intended. Here's another example using the 'Sketch > Reticulation' effect (again zoomed right in so you can see the pixels):
Each time the effect applies as the circle is scaled up, it re-interprets the effect, filling the circle with a greater number of gravelly bits in a new pattern that works at the same resolution.
So, you can 'infinitely' scale up a vector shape with a photoshop effect applied without worrying about resolution issues or data loss as you would in Photoshop working with raster data. But, you need to keep an eye on how the effect is applying itself each time, to make sure it's not re-interpreting it in a way you don't want. If it does, you've got two options. You can tweak the settings to better fit the new size, or, you can go back and 'fix' the effect into pure vector data using live trace - depending on what you want in each case.