If you are Capturing a Payment, yes, the client will receive an email notification with a link to print the receipt.
If you are Recording an Offline Payment, no, the client will not receive a notification.
Here's what will happen after when you either capture an online payment, or record an offline payment
If you are Capturing a Payment, yes, the client will receive an email notification with a link to print the receipt.
If you are Recording an Offline Payment, no, the client will not receive a notification.