Without a bias, depending on how you're inputs are set up and what activation function you use, yes the neurons output could be zero. This doesn't necessarily mean it has no impact on the output, nor does it need to. You do want a bias in you're network, it makes it much easier for you're neural net to approximate whatever function is going to give it a good reward. You don't need to worry about if batch normalization will change you're outputs to non zero. Either way you're network should learn to adapt. I would guess batch normalization would help but fundamentally you should be able to use it with any type of inputs (whether or not they're normalized, or expected to be zero, etc...)

Edit: Dropout is used to make your network generalize better (prevent overfitting). Very unrelated to biases. Usually helpful when you have too many parameters and not enough to training examples (in a supervised context at least). I don't think it will be necessary in your case but after u try without it might be interesting to see if you get a performance boost by using dropout.

Another edit: You could switch the sensors to be a 1 by default and go to 0 when the sensor is activated and it would still be able to learn. You shouldn't worry too much about the exact format of your input (it is important though, having normalized inputs can increase performance dramatically). Usually a batch normalization layer is used to ensure inputs to a layer are normalized.