When things like the new free trial limit get announced, I always automatically assume the developers know what they are doing. They would never overlook something as big as trial accounts being able to buy houses, unless they wish for them to be able to.
So they will either make it so you can't buy houses/apartments, through restrictions or just through the gil cap (even if that could be somewhat unsafe maybe), or they will outright allow trial players to buy them. But I don't think they will. Why would they even do that?