Does Aperture 3 offer any way to get the size (in B/kB/mB/gB) of a batch (i.e. selection or event) of versions from within the application itself?
No, you can show the filesize for a single original in the metadata panel, but versions do not exist as files, until they are exported or shared. So they simply do not have a filesize. The file format, the quality, the dimensions of any rendered version will only be determined when you select an export preset when exporting the file and creating it.