Hi Jordan,
There's nothing inherently preventing you from configuring settings, or registering classes with the pool at any time. As Aaron mentioned, you will want to do things in a specific order, regardless of timing in relation to other events.
Registering a class with the pool is typically done at the start of the game, before switching to the first state. This is just done as a matter of convenience; it's part of the game's initialization, not part of the play screen's initialization.
For some general background information: The object lifecycle within melonJS provides a few different events which are triggered at different stages of the lifecycle. For example, init is used as the object constructor, and is only called once for the entire lifetime of the object. onResetEvent (aka onActivateEvent) is triggered every time the object is added to the scene graph, and onDestroyEvent is triggered when it is removed. This provides events for "soft" initialization and destruction. E.g. for resetting properties on the object after it has been recycled into the pool.
A less complex approach is to just not use the pool; let JavaScript run its Garbage Collection to free memory automatically when objects are removed from the scene. This will incur a performance hit, however. And some objects like me.ScreenObject are never released to GC...