Yes it can. It requires a bit of setup from your side though.
To do this, visit your account:
construct.net/en/game-services/account
Go to your game, then on the left menu select Auth Settings. Scroll down to Google, and enter your own client ID and secret.
You'll need to create your own Google client ID/secret from:
console.developers.google.com
And during creation of your client ID and secret, you must enter
auth.construct.net/google.json
As an authorized redirect URI.