Can I get the optional media update for 360 without xbox live?
the short answer is no. it is only possible to download system update from xbox.com and install after burning to disc.
if your question, however, is asking if free account (i.e. silver account) is eligible for optional media update then the answer is yes. you just have to have an internet connection.
if you need to bring the machine to others' home for installing this (just in case you can't install the internet on the xbox, etc) then bring the whole machine, not just the harddisk.