Congratulations, now all of your email goes to a single different email address; your tracking profile is now associated with randomstring@email instead of john.doe@email.

If you wanted something truly private you could create an account at a provider like Fastmail or ProtonMail and create an alias for each account (or just wildcard a custom domain until you need to send from an address). I doubt any tracking system is based on the domain in your email address... not yet, at least.