It's MIT/Apache 2.0 licensed, so yes. However, because it's also an open protocol, even if it wasn't, you could write your own under whatever license you want.
> What's the difference with Bluesky?
BlueSky is built off of an open protocol, called AT. https://atproto.com/ BlueSky is a particular app built on the protocol. As such, there's no way to "turn off the API," as BlueSky itself is a participant in the open protocol.
They could like, re-write everything to be a central service, port the user data over to it, and then pull out from the network, but then two things would happen:
1. stuff would break, as it's no longer part of the network.
2. since there is true account portability, users could simply swap to a different PDS and client, and re-route around the damage.
Also given that it's against their entire stated mission and goals, it would be social suicide.