Technically yes. I believe it’s been said in the past that if an amazing complete game is submitted they may be willing to consider it for the official label.
But in practice Choice of Games and Hosted Games operate differently so there’s no real benefit to doing things that way. For the Official label games they have a very clear vision of what they’re looking for in games, and they work with the authors to enable them to achieve that.
For the Hosted Games you get total creative freedom over any game you’re creating, no deadlines, no one telling you what to do.
And Choice of Games do ask you not to send them games, or games pitches first. They want a cv, and then some concepts, then a game outline, and only then, once they’ve approved each stage, do you start actually writing the game.
If you’re interested in writing a game under the CoG label, please email us your CV to email@example.com; if we decide to move forward, we’ll ask you to send us some game ideas. (Please do not send us a pitch before we ask for one, even if you have a really great idea. Just send us your CV.)