Maggie, campaigns will send emails twice if this is normal program. Though they are members of program and sharing same email, there is no restriction on duplicate email. If you are sending email from engagement program, then it will not.
Depending on how your campaigns are set up, you can always add a smartlist list filter on both campaigns to include "Not Was Sent Email: xxxxxx". That will make sure the lead doesn't receive the email from two different campaigns. Hope that helps!