I don't know. A VPN simply replaces your IP with one from their network, but you still have one IP that identifies you, right? So if you are using one tool to access YouTube while being logged into Google on your browser, doesn't that defeat the purpose of the VPN? I mean if Google just stores the IPs that were used to log into accounts they can simply look up who downloaded their videos, right?
Unless you actively pay attention it's very easy to be logged into some Google service without noticing. At least I wouldn't be surprised if chrome background services kept me logged into my work Google Mail account and kept tracking my IP.
The biggest question is how meaningful the IP alone is. I don't know if VPNs assign people individual IP-adresses or if there's some kind of NAT in use where people share an IP with translated ports. If the information is "there's this individual VPN-user and we need to connect them to a name" then you shouldn't use (the same) VPN for everything, but if it's just "there's another request from the same VPN" then it's fine.
Can you elaborate?