In my own experience you can simple copy paste the entire Steam/Valve folder and run it from it's new destination.
Hence, yes you can just copy the entire game's folder with the updates to the other computer
And I just stumbled upon a Super User question about this. Quoting John T:
I do this all the time it is fine to
do. Any files that do not match are
usually re-downloaded from Steam,
hence why it will still update a bit
after a fresh copy. If you do not want
all the sounds and maps which take up
a lot of space, you can simply take
the .gcf files for each game from
Program Files/Steam/SteamApps, these
are the biggest files in the update
which will save the most time.
Steam also has a "Backup" feature you
can use. The files it creates can be
moved from PC to PC and restored on
any one.