You can fund and invest on the same day. To make a POLi-supported deposit: On the Stake app, head to your portfolio dashboard and tap Buying power > Add funds on web, click on the Wallet icon in the right hand corner > Add funds. Insert the deposit amount.
Does Stake.us pay out? Yes and no. Stake.us doesn't pay out real money for wins on their site. They award Stake Cash, a type of virtual currency which you can collect and redeem for gift cards, cryptocurrency, and other rewards.