Sure, that's why the choice of VPN provider is important. You need to choose a provider which doesn't keep logs, and has the character to shut down their business before being legally compelled to reveal users, like lavabit did. You can read this thread for an example: https://airvpn.org/topic/15396-does-airvpn-log-its-users-ip-...

For additional protection, you can also run Tor over VPN.