I haven't added an email program to an engagement stream before, but I would recommend just keeping the 3 emails in the stream. If the intent is not to have the lead receive Email B or Email C if they have already opened the previous email, then I would instead change the engagement program cadence to "paused" if the lead does open the email. Have a separate smart campaign look for "opened email: Email A" or "opened email: Email B" and the flow would be to pause them (change engagement program cadence to "paused"). What this will do is once the lead opens Email A, they will not receive Email B or Email C and if they do not open Email A, they will continue to receive Email B at the next cast.
The cadence would roll ever onwards, regardless of where they are in the previous flow... so to answer the question behind the question, yes, you'd jack up your cadence. Think of them like separate smart campaigns.