If you find an anonymous, unconnected candidate (e.g. someone who is registered with Not Actively Looking, but not connected to your firm) during the search process you can still add them to assignments – they will appear in the 'NAL Invites' tab on the assignment until the invitation is accepted.
Doing this automatically sends an email suggesting to the candidate that they connect to your firm but it does not make any mention of what the assignment is and it makes it clear that your search firm may not make any further contact. It just means that you have another connected profile (with full profile details) that you didn’t have before, but you are not under any obligation to do anything with it.