I worked on this with support and wanted to give updates to the community.
Parent my token will not pass to the emails but the program token will.
So if it is something like program name or program description, you can plug it into emails.
Just built a test scenario for this and I'd say that this doesn't work. Neither local nor inherited program tokens are being handed down to the email from the executable campaign.
A team member had a good idea this morning:
No, you cannot render program tokens through executable inheriting on the email directly, but you can paste these tokens into PMCFs and use their tokens to populate the email.
That process works with local and with inherited program tokens!