If I place a program into an engagement stream (say that program has a smart campaign with a specific smart list) what happens if a lead does not qualify to receive content because they did not meet the smart list qualifications in the smart campaign? Does that still count as a "cast" for that lead, even though they did not receive the email? Do they just skip to the next piece of content?
Yes, this counts as a cast.
Is the qualification a rule that they can qualify later in the engagement campaign? If not, the leads that did not qualify to the receive the current cast can be move to the next cast without the wait. In the Admin section, under your Tags --> Channels, you need to add a stage like "Exclude" which should be the last stage. And when the leads do not pass the qualification, change the program status to "Exclude".