Is it possible to put the alpha game on Steam or something out of curiosity?

You mean a game in the alpha testing stage? I've seen a few of those, typically ambitious multiplayer ones. Might be more accurately described as beta, but it's just a word.
Haven't had dealings with steam, but it's likely a matter of the content being sufficiently stable for the users to try out. They get their cut, they don't care whither it comes so long as it doesn't reflect badly on their reputation.

Example:
https :// store . steampowered . com / app/1341330/Gatewalkers_Alpha/