The opt-in window and its submission are all handled by Google, so if the opt-in is appearing, the data will be going to Google successfully.
As for the email not arriving, this could be one of two things, which are both in Google’s control. Firstly, Google doesn’t necessarily send an email to every customer who opts in. Looking at my own stores reviews statistics, it would seem that about 90% of my customers who opt in eventually receive an email. Secondly, Google waits until after the estimated delivery date before sending the email. So if you have set your estimated delivery days to 2, Google will wait at least 2 days before sending the email.
Review opt-in and survey statistics in your Google Merchant Center account can be delayed by up to a week, which may explain why nothing is showing in your Merchant Center yet.
This is what Google says about the matter on their troubleshooting page:
Ensure that the ESTIMATED_DELIVERY_DATE for the order has passed. Customers who opt-in to the survey receive an email that asks them to rate their experience in a few days after the estimated delivery date that you included for the order in the survey opt-in module.
Additionally, the information shown in Merchant Center graphs can be delayed up to 1 week.
