the_crippler :
Even backing up and transferring the game would still cause it to go into check mode on the game files, which also generally takes a long time.
Checks aren't done by downloading the entire file again and comparing. The file is read on your computer, a checksum is generated, and the checksum is compared to the "correct" checksum for that file on the server. Only if the checksums are different does it download the file again. If the check is taking a long time, it's because you have a slow or fragmented HDD.
So yes, updating it on one computer, then copying the steamapps folder to the second computer will eliminate a redundant download on the second computer.
If you have a laptop, install Steam on there and copy the Steam folder from your desktop. You don't actually have to play games on the laptop, you just want Steam installed. Go visit a Starbucks or McDonalds or someplace that has (fast) free wifi. Update there. Then go home and copy the updated steamapps folder to your desktop.