NO, Your PC can't even access Xbox LIVE content, let alone let you copy that
content from your PC to the 360.  You can't even copy content from your 360
to some other external HDD plugged into your 360.    Soon when the new 360
Dashboard is online you can BUY content on your PC and get it later on your
360.   I would guess you'd be able to view what was on LIVE, but there's no
downloading onto your PC.

MS does allow you to download system updates for example, which you can then
burn on a CD/DVD for example and pop it into the 360 and install it for
those people that don't have LIVE access on their 360's.  You can even get
the Updates if you bring your Memory Card to Best Buy for example and pop it
into the 360 Demo case where the slot is for the Memory card and get Updates
that way, if it's working and what you can get varies from place to place
from what I hear.