Leads can be part of multiple engagement programs at a time.
Leads won't be added automatically to your new program. You'll need to configure a triggered or batch smart campaign with entrance criteria to add people to a stream in the new engagement program.
I would suggest mapping your existing programs to the new streams and then setting up a series of campaigns to add them in once you turn off the old programs. You'll also need triggered campaigns to ensure leads are routed into the correct stream automatically going forward.
Hi Melissa, to clarify on what you probably heard, leads can be a part of multiple engagement programs at a time but they can only be a member of a single stream within a specific engagement program. Best of luck with the new programs!
As Justin commented, leads can potentially be members of multiple engagement programs. You will need to build what I like to call "back fill" smart campaigns and even a traffic cop to get all your leads into the correct new engagement program on an ongoing basis.
An engagement program DOES protect you from sending the same email twice to a lead so long as the email is in that engagement program.