Latency in this case would be the time it takes for your device to ask the raspberry pi what IP address is www.google.com and the pi will reply to the device with the IP address.
I think you might be misunderstanding how the pi hole blocks adverts.
It doesn't filter http traffic by looking at the contents but instead has a block list of domains that server adverts.
When a device on your network requests the IP address for a blocked domain PiHole just replies with a fake IP (or nothing, I'm not sure)
Pihole/dns wont realistically be affected (DNS is a tiny amount of traffic). But running a VPN ran on the pi will be limited to the Pis max performance. As long as your CPU isnt getting pegged at 100% or thermal throttling other services shouldnt impact pihole performance significantly.