Ipad PRO 12.9 as second screen on macbook pro while using a VPN

There are third-party programs that you can get (or rather, pairs of programs - one for Mac, one for iPad) that work like Sidecar by cable. You would have to research whether they need to use local wifi at the same time.

One that I have used is called Duet. I have not tested how it interacts with a VPN, but it does work across a cable when both wifi and Bluetooth are disabled on the Mac.

Short answer - no.

iPad does not provide any facility for direct video input.

Without delving too deeply into the intricate details of VPNs and secure networking, perhaps suffice to say that whilst your VPN connection is active, Sidecar will very likely be unusable with your Mac and iPad.

Sidecar must be able to communicate between your Mac and iPad using its network connection. Whilst your VPN is not active, the two devices - when connected to the same WiFi Network - can freely communicate. When your VPN is active, this network communication is interrupted.

In greater (but non technical) detail...

Imagine that your VPN provides a pipe (a “tunnel”) through which all your network traffic from your Mac must flow. Unless this secure tunnel has a “leak”, no network communication can take place between the Mac and the iPad - as the iPad has its network connection that is outside of your secure tunnel connection.

Some VPN configurations allow a feature known as “split tunnelling”. This configuration allows network traffic to be sent either through the secure VPN “tunnel” connection, or to the local network. Whilst this type of VPN configuration will permit Sidecar to simultaneously work with your VPN connection (the connection has a “leak” to your local network), it can be insecure as sensitive network traffic may be routed outside of the secure tunnel connection. Many corporate VPNs will not permit split-tunnelling.

Your USB connection, whilst using a cable instead of WiFi, is still providing a network-interface connection between devices. If split-tunnelling is inhibited by the VPN configuration, the Mac and iPad cannot directly communicate.

I hope this explanation provides some helpful insight and understanding of the functioning of your Mac VPN and its interaction with iPad and Sidecar.