Since you can charge with the new iPad Pro, I was wondering if something similar could be done using the lightning to USB adapter and the charging cable
Yes, you can use an iPad Pro to charge other devices, including an iPhone.
According to Apple:
To charge your iPhone or earlier-model iPad that has a Lightning port, connect it to iPad Pro using the Apple USB-C to Lightning Cable. If you have a Lightning to USB cable, you can combine it with the Apple USB-C to USB Adapter, then connect the adapter to iPad Pro.
Source: Charge and connect with the USB-C port on the new iPad Pro, Apple, [Bold emphasis mine].