Printing to a Local Printer While Using VPN
This largely depends upon the settings that your network administrator has set up for your VPN connection.

It is possible for them to require that all traffic travel through the VPN tunnel, at which point, no, you will not be able to connect to a networked printer in your home.

It is also possible for them to allow traffic that is not bound for your organization, to be transmitted outside the VPN tunnel, at which point you should be able to access your network print and other network resources in your home.

I would check with your network administrator on this...  he/she will be best able to help you out.