VPN over ethernet, Internet over wifi
Depending on the VPN client being used, this may or may not be possible. Certain VPN clients (like Junos Pulse, for example) can be set by your network administrator at work to enforce certain routing policies when connected via your VPN client. If your sysadmin at work set your VPN client to force all outgoing traffic to go through your VPN then you're most likely out of luck (I know that Junos Pulse can be set to automatically disconnect if the routing table is touched once connected). As your sysadmin at work how it's configured.