Yep, that should do it.
Some people only download their Kindle books to their computer from behind a Proxy Server which makes it appear like their computer's IP is in the US. Some people don't and get by just fine.
Buy your gift cards out of your German Amazon Account, email them to your German email address ... and then go into your US Amazon account and apply that Gift Card number to your US Amazon account. That is how you will pay for your US Kindle books.