I've tried this a couple of different ways with no success. I can hardcode the "to" line for the customer email notification and it works fine. But if i try to use a variable - like the customer's user-entered email address - no notification is received. In CartTrhib's order settings, I have the "Customer Email" field mapped to my custom field in my orders channel. It's being captured and shows correctly within the email notification itself. But I don't seem to be able to use it in the "to" field for the email notification's settings. Are custom fields - even a mapped one like customer email - not available to use?
Just wanted to provide some additional information on another way to solve this problem (for those who aren't familiar).
Postmaster v1.2 provides CartThrob integration support out of the box, and the next version (1.3) will bring things like Abandoned Cart Notifications for which CartThrob now charges $500.
Postmaster is definitely a premium solution and at face value can seem like more than one might need. But the template tags and options for CT are much more complete than what they even provide. I designed Postmaster to make scenarios just like this a breeze to fix. It takes just a few minutes to advanced templating with CT setup with any email service you desire.