No, you have to publish the game in both places.
If you get to the deadline, and you're about to run out of time, always submit your game to itch.io first.
itch.io locks submissions during the voting period, so we can be 100% confident that a game isn't tampered with during the community voting period, without having to check every single game. That version of your game will be the one that people will play and vote on.
But if you don't have the gd.games version of the game uploaded by the end of the voting period, we won't count it as a valid submission.
We make some exceptions when someone is having trouble submitting their game to itch.io because of something on itch.io's side of things, and allow them to submit the gd.games version of their game as their "browser version", but they'll still be required to upload a downloadable version of their game to itch.io, to prove the state it was in before the deadline.
I hope that helps. 👍