Mob spawners are still active. Even though you cannot 'own' a mob spawner, you can still build around one.
Mob spawners are considered public property regardless of what someone does to the surrounding environment (since they are naturally created by the server)
But to the topic at hand, an arena wouldn't be so bad, yet you would want to have more than one type of mob at an arena, since fighting just one type of mob would get boring pretty fast.
And as what PsYk0 said, you can create mob traps pretty easily.