Nope, this isn’t supported, as the Gold Saucer minigames feature is pretty tightly coded to the location in the Gold Saucer.
Enabling it for housing would be quite a lot of work, which would take several weeks of development for no real advantage.
Very few things in the game are auto-moderated by Square Enix, like your character’s position (which is why teleporting hacks get pretty much instantly detected and users of those autobanned in a short amount of time). Housing areas are allegedly also one of those things that have auto-moderation to catch people non-stop crafting the same thing 24/7 in their closed house, and it’s likely that housing gold saucer minigames are also auto-moderated.