Glad to know that you have your problem solved. Cheers!
Yes. It makes sense.
This is the way of how to convert a USB laser printer into a TCP/IP (i.e. network) printer (connect to a printer server).
First, install the laser printer by USB port (direct to a PC) using the supplied driver CD. Second, attach the laser printer to the print server. Finally, change the port from USB to a TCP/IP in the PC.
But, for scanning, I do not have a HP All-in-One printer to try, but it is good to learn from your case that printing and scanning do share similar workaround for getting the setup done through network.