Is it absolutely necessary to season a carbon steel pan?
I would never leave it unseasoned. 

Carbon steel rusts. If you just cook with sufficient oil, and let it cool down with the oil still inside, and then clean gently (preferably without any soap), the inner bottom will indeed session itself with time, as tfd mentioned. But the rest of the pan will be exposed to the air and will create a layer of rust. If you don't use it frequently enough, or if you prepare acidic food in it before it has gathered some seasoning (and most vegetables are acidic), you will get rust on the bottom too, before seasoning has had time to build up on its own. 

Ingesting rust is not an immediate health risk, but it is better to avoid it. Our bodies weren't designed for it, and you might end up with too much iron in your diet. It is also porous, so the pan would be hard to clean well. And it looks really shabby to have a rusty pan in the kitchen. 

And if this is your first "normal" pan after years of non stick, you might be amazed at the amount of oil needed to prevent food from sticking. It looks terrifying to our modern "fat is bad" eyes. And you still have to be careful, despite the oil. With time, you will learn to cook the right way, but having it seasoned first certainly helps. 

There is no law requiring you to season, but to me, the above reasons are enough to always season.