YES, your restaurant can survive without a marketing strategy.
As long as you have a great product, you can coast through like a glider in the sky. Just like a glider needs help from Mother Nature to stay in the sky, you will solely rely on word of mouth, which is out of your control.
However, adding a sales and marketing strategy is like putting engines on your glider. Yes, there is an investment, and you need to be consistently adding in fuel. But you can control the speed, the altitude, and the destination.
Instead of just surviving like a glider, wouldn't you want to accelerate your restaurant growth by having a sales and marketing plan?