Since I originally posted the thread I've come to discover that in principle it is true that furniture can be had for cheap, as people do leave the city all the time. The prerequisite for taking advantage of this is having 1) time 2) own transport 3) patience to hunt down the furniture you want piece by piece. For many people it all ends up being too much of a bother - they go over to IKEA and _done_; others run into arrangements where they seemingly get off for little money buying used items from someone leaving, only to replace much of the stuff bought within a few months for reasons of aesthetics, usability, durability, etc. A question mark over cost-effectiveness there, when all is summed up. Added complexity if you know you'll be staying in GVA just for a couple of years.
In view of this, I do think there's a "niche" here for a serious business that would offer turn-key furniture rental, good quality / reasonable price. Most of those that I've managed to track down, and which had a b2c model, were not-that-great (price, service, range...). The furniture on offer would have to be of quality, so as to differentiate the service and hold value over time (= no IKEA/Conforama). This may or may not imply a considerable up-front investment.
It seems logical to me that to make a real business out of it one would ultimately need to work directly with those in control of empty apartments (e.g. régies, businesses), switching over time to a b2b model. There you enter a who-you-know sort of a business, given GVA's feudal real estate market. I'd be surprised if a few such b2b operations didn't already exist, I'm just not likely to be privy to them.