I think what you need to do is say what you want to use the logo for and why you want it to be transparent.
Illustrator can do all that kind of stuff and unless you put a solid background on the logo it'll preserve transparency as a .PDF but...
Only when opened back up in Illustrator or something like Photoshop.
If you open a .PDF in say Preview it will appear to have a white background.
If you were using it for something like the web you could save it as a .PNG that will preserve transparency but it will be a raster image (pixels).
Again, it depends what you are using it for.