Yes, you can add (Drawable)GameComponents at any time. When you add them before Game.Initialize (eg: in your game constructor), they will have their Initialize method called when Game.Initialize is called.
If you add them after Initialize is called on your game class, then they will have their Initialize method called when they are added to the Game.Components collection.
Note that the upshot of this is that there is a small window in your game class's Initialize method, in between you calling base.Initialize() and returning, where game components will not be initialized!
Note that Game.Initialize will call LoadContent, so adding components in your LoadContent method also will cause them to not be initialized. Although adding components from a game component Initialize method will work.
DrawableGameComponent.Initialize calls DrawableGameComponent.LoadContent (so don't skip any base calls in methods that you override).
You could also add them at the start of your game and then toggle the Enabled and Visible properties as required.
Alternately, you could skip the game components system all together. It's basically just a list of objects with virtual Update and Draw methods (et cetera). This way you can program things to do exactly what you want.
