Not in the usual way. Participants Database is not set up to be a mailing list manager, but you can get some similar functionality with a special configuration.
One approach is to add a checkbox field to your database for the user to check to opt-in.
With a typical Participants Database setup, when someone registers, they get an email with a private link to their record. They can make changes to the record on that page. This is where they would click the checkbox indicating they want to opt-in.
After that, you can use that value to filter out records that have not been opted in.
The article below provides a lot of detail that may not be relevant to what you’re trying to do, but it does describe how to set up a formal opt-in such as what is required by European GDPR regulations:
GDPR Compliance and Participants Database