assuming your building is on 3 phase, and most apartments would be 2 phase you might end up with a problem, but it does say works across phases so it is possible it might work anyway. As long as you are on the same phase the only place you would have a problem is the transformers on the pole, so I would get two and try it in various plugs throughout the building. I suspect that it should work. as for the phone line solution, that does work but it can get messy, especially if someone tries to rewire the phone. If you only have 2 lines they make etherenet extenders which work over a single pair and are esentially dsl modems done back to back, they are single duplex which means you send and then recieve but they will work better than dial-up. They may have come out with full-duplex models by now but I havn't had to play with them for quite some time. There is always the wireless option but in older buildings it can be problematic and will require some boosting and at least a passing familiarity with wireless security, and hours of helping people get setup, over and over and over again.
best bet: buy 2 and try it out.