While there are many steps involved, the process of inviting an existing account is a relatively simple handshake process. This means that both sides must actively initiate/accept the invite, in order for it to succeed—an invite cannot be forced.
After specifying the target account's account ID (or e-mail address), the e-mail address associated will be notified.
As part of the handshake process, the invited account must explicitly accept the invite.
It is important to note that the default invite type (and what we have used in the recipe) is to use the full feature set for AWS Organizations. As noted in the console, this means that the invited account could be prevented from leaving the organization if the relevant policies are configured.
After confirmation, both parties will receive an e-mail detailing the membership. From this point forward, the bill for the invited account will be paid by the master account.