IF by the Internet you mean the Web, then the PC uses the faster connection by choice (metrics of transit times). Usually when some one says "VPN" they are referring to a connection from home or hotel to a company network. Most do not pass Web requests to the company connection. If you are using a DSL/cable modem and then running a VPN to the office, the Web requests should never go through the VPN. That would be an extra transit or two for the connection. If you are using dialup direct to the company network, you may be allowed Web access, but at dialup speed.
This was first published in October 2005