Yes, that's possible. Checking the cookie and the email should just be a single auto action. You'd check the cookie in a Condition and the email would just be an Email action. You'd use the onAfterUserRegistration trigger. Example as follows.
Global
Trigger: onAfterUserRegistration
Type: Email
User: Automatic
Access: Everybody
Conditions
Field: Custom > Value
Custom Value: [cookie_COOKIE_NAME_HERE]
Operator: Not Empty
Action
To: YOUR_EMAIL_ADDRESS_HERE
Subject: Cookie Registration Detected!
Body:
Code:
Registered Username: [username]
Replace COOKIE_NAME_HERE with the name of your cookie. Replace YOUR_EMAIL_ADDRESS_HERE with the email address you want to send this to. It should send the username of the newly registered user.