Yes, with the right setup you can exclude an application from using the VPN. However, Private Internet Access does not provide support for this.
By default, PIA sends all your traffic over a secure encrypted tunnel. Excluding an application from the VPN connection is done by a process called split tunneling. If split tunneling is used, specific apps are excluded from using the VPN. The traffic for those apps will not be encrypted or protected by the VPN.
While this setup is possible, it is typically very complex. It also provides a direct link from the outside network to your machine.
Because of the complexity of the setup and the possibility of leaking data outside the VPN connection (which can introduce security risks), we do not support split tunneling at this time.