When customer abandons paypal checkout, will the responses still be recorded on my end?

I have PayPal on my account. Let's say someone goes through the form and clicks submit, and is later taken to the PayPal external page but they change their mind and X-out of the form. Will the responses still be recorded on my end?

Yes, it will end up in your incomplete payments list which can be viewed in your form submissions page. 

http://www.jotform.com/help/135-How-to-View-Pending-Submissions?

If you want to get email notification on incomplete payments, check this guide https://www.jotform.com/help/273-How-to-Setup-Incomplete-Payment-Notification-Email