You can have your other email sending campaigns/programs are checking to see if someone is a member of the engagement program and not send if they are. Assuming you can find the other campaigns, that is probably the easiest option.
You can view the membership of a stream within a smart list. The esiest way to ensure that someone doesn't receive an email is to exclude them from the blast within the smart list, using Member of Engagement Program filter. If you want to be a little more complex, you can create your own version of an email management system where as you "opt-in" Leads to your Nurture and when you opt them in, you simultaneously opt them out of other campaigns. This would take quite a bit of time to set up and would require backtracking.
Do you have any other automated campaigns?
You can probably add them to a specific list that will block them from receiving other emails.
Using a filter on all other email programs would be the best, most reliable way (as described above by Jeff S).
However if you'd like a simpler (but less reliable) way to do it globally from the engagement program you could mark all active members of the Engagement program as Marketing Suspended except when the program is scheduled for a cast.
So all members of the engagement program who are neither exhausted nor paused would be marked with Marketing Suspended = True until just before your Engagement program cast. Just before the cast you would set Marketing Suspended to False (otherwise the engagement program won't send them an email) and then once the cast is complete mark them Marketing Suspended again.
Leads that are in the engagement program but not receiving emails (exhausted or paused) should not be marked Marketing Suspended.