You have to call al_init() and al_init_primitives_addon() exactly once before using any Allegro primitive functions, that is basically your only rule. Therefore, you don't have to call it in your main function, as long as you call it somewhere in your main thread, so you COULD, in theory, put it in the constructor of your circle class. This doesn't sound like a good design choice, though. Simply speaking, "initialising Allegro" and "drawing a circle" are two completely different tasks, so why would you want to do them both in one class? This would get especially messy once you added other primitive classes, like "line", "rectangle", "triangle" etc. Basically you would have to put that code into the constructor of each primitive and still somehow make it execute only once. And if you ever had to change one of the constructors to fix something, you would have to change the other constructors as well.

Why not just call the init functions once at the beginning of main and then only put the actual drawing code in your circle class? Or, if you absolutely, for whatever reason, want to hide all Allegro functionality in classes, make a second class called "Application" or something like that and give it a static function called "Init()", where you put the calls to the Allegro initialization functions, then call only that Init() function in your main.

The usual way would be that when it is time to render, the engine gives you a GraphicsContext* that is assumed to be valid. It is up to the engine to do any preparation so that the context is valid at the time you need it. Usually when your game engine starts, it initializes any global or thread-global state like Allegro and its addons.