Yes, I do it all the time. THe only downside is you have to download the patches twice. So be prepared for a looong install
If it downloads an actual file (which is generally what happens with the larger patches), I just copy the file from one computer to the other.
You can check the root of the WoW folder for the files; I have all of them on my spare PC so I can burn them onto a CD if needed. I also delete them off the computers to save disk space (its 151mb!!).
 here are the files thus far: