Here you should not use live mail applications (like gmail, yahoo mail etc..) for performance testing purpose as those are 3rd party applications.
Other alternatives what you can do is:
1. Make the verification code as static, so that you can hard the verification string, and use some test mail like testuser1@perftest.com so that it won't load any live applications
2. Request developers to print the verification code some where in the response so that we can capture and pass it to the next request.
3. If possible skip that verification step with the help of dev.
Thanks, Ajay