It will really depend on the fine details. If Amazon would lose its military contracts unless it dropped Claude, then Claude will be gone tomorrow. They just got a half billion contract for the Air Force earlier this year, and it's not their only military contract, and they're going to want to be well positioned next time something like the JEDI contract comes along.

Also, AWS has a long history of rolling over when politicians make noise about AWS customers, going back to when Joe Lieberman casually asked Bezos to please stop supporting Wikileaks.