I am doing something similar to this, but for my fulltime build. I maintain a server at a location with all my storage and fiber internet. All my roms are located there, I used a i7 high powered intel NUC as my Launchbox PC and set BigBox to run on windows boot, so no Windows GUI displays at all.
I have a VPN connection that starts when the PC boots automatically and my roms exist on my network drive. So far I havent had any issues. Even playstation 1 games load pretty quickly. You would do the same thing on a phone with VPN connection if you wanted. But obviously data usage could be a problem with large games.