Yes, absolutely. I do the same thing, every time I go online with my X360.
It's very simple, but you can hit some snags along the way:
#1. Depending on the gateway settings, you might need to shut off his computer, remove the router access to the computer, and plug your X360 into his routed (if a router is used).
#2. Turn on your X360. It will automatically attempt to sign into XBL.
#3. You might need to troubleshoot a few issues to sign onto XBL. I know I had to work with DSN settings, IP addresses, and such. I eventually "fooled" the router into thinking that the Xbox 360 was the computer, so it signed me on pretty easy.
#4. Create a XBL account. You DO NOT NEED a credit card to do this.
#5. Add a credit card for Microsoft points. Or you can just go out and buy the MSP at any store, or Ebay and just "redeem code" to get the points. Typically, the later ((Ebay)) is the cheapest route.
The GTAIV content will either be free if you pre-order (supposedly), or will come out in Fall 2008. So be prepared for that.