SpaceX will absolutely sell them boosters to do this. Here is why:

1. It's regulatory top cover. "Starlink is not a monopoly, we have competitors <points at amazon>. We launch competitors satellites as well."
2. If Amazons effort fails, they can buy it for pennies on the dollar while still having gotten full price for the boosters.
3. If they decide to divest Starlink, it provides them a mature acquisition candidate.
4. They get to sell their competitor boosters at full price while launching their own satellites at cost.