No, they could get billions to fund the rest of the business with by selling it. It would be a huge IPO. Potentially wirth more than the profits.
AWS is eventually going to be a $30 billion sales business, capable of generating $3+ billion in net income. It'll legitimately be a nearly $100 billion market cap company unto itself in ten years. If Amazon is smart, they'll wait until it achieves a much larger scale before spinning it off, it's obviously a huge pot of gold in the equity value.
Amazon Web Services, Inc. is a separate corporation wholly owned by Amazon.com Inc
I agree, it seems unlikely in the near future given Amazon's history, but it could happen. Maybe 10-20 years from now when Bezos has retired, a new CEO or three has been in place and the public markets aren't as forgiving of Amazon as they are now.