Yes, but Minecraft was on sale for a year before it ever went into "Beta," back before it was in Alpha even. In fact, it wasn't until one of the last Alpha updates that the earliest semblance of "Minecraft" as we know it really began to appear. The Beta updates added a lot of core features we take for granted in the game, like beds for sleeping, tall grass for seeds, redstone repeaters, pistons, sprinting, hunger, etc.

The first purchasable version of Minecraft I remember didn't even have a working health bar.

Notch sold the game to Microsoft long before it was ever a complete game. Why program something when you can sell players on an idea and then sell that idea to Microsoft?