Schedule reoccurrence of smart campaigns to add engagement campaign members

Hi,

I'm using a smart campaign to add people to an engagement campaign based on their account type. We had the campaign set up to run a single batch to add  people with a specific account type to the nurture campaign and then based off of triggers, add new people. The triggers from Salesforce don't include what I need - I need a trigger based on a new account being added, not a new lead. So, I'd like to just continue to run the smart campaign and add batches on a weekly basis. As you can see, after running this smart list of Friday, I have over 100 new people that could be added to the nurture campaign.

If I schedule a reoccurrence, would this only effect the people with new accounts that meet my criteria? Also, I want to make sure that the existing people in the campaign don't get sent through the engagement campaign again. Would this work to continue to add people to the campaign on a weekly basis?

Thanks in advance for any help!