Printing to a home printer from a work Horizon VDI

Suppose you were a home user with a VMWare Horizon client for accessing your work virtual desktop. You have an HP printer scanner and you want to print via a print server at the data center. If you setup a port at the work firewall - would it be possible to configure a printer to register with the file server with authentication? The net result being that the home user logins into their VDI and prints to their home printer via the print server in the data center.

Is that possible and done all the time? I have small offices with lan to lan VPN and that's easy to just enter the IP of the destination printer.