I have been testing version 2.3.7 on a Joomla 1.0.15 site.
I have two payment methods for an event. The pay later version works as expected and adds the user to the Registration Record. I have tried the Paypal test mode with a sandbox account. It connects to Paypal sandbox and all that works and then it returns with a thankyou etc.. But the user registration info is not added to the Registration Record info. I checked the datbase tables and the paypal session table does have the info. But it does not add the info to the user table so consequently does not show in the Registration Record screen in the backend admin panel.
Test mode is not intended to run the full process... just to make sure you are connecting with the payment solution. Running in live mode, your records will be created just fine.