A small one, yes. You can store things in an apartment that noone else can access (both equipment and cases). You can also have your own private chat room, message board, or bookshelf if you want one. But apartments (and the furniture to decorate them with) are ultra-expensive, and I believe only subbed people can get them.
Basically, they're a thing to play around with after you've picked up all your skills and are an experienced and veteran player. They're an expensive hobby. ;-)