op amp level shifter no input situation
If the input is disconnected, if that's what you mean by "no input", the output will not be midscale on the ADC. It will be indistinguishable from a 1.6V input. 

You can deal with that by buffering the input (voltage follower) and adding a high-value resistor to ground on the input of the buffer, but you'd need power supplies higher than +/-5V for the buffer amplifier (how much higher depends on the op-amp used). 

You can also apply a reference voltage other than ground to the left end of R1 in your top diagram, but it will have to be a negative reference voltage to shift the output above ground. That would allow a single op-amp with a single supply, but you need a negative reference voltage. 

You could also add a resistor from the ADC input (right hand side of R? on your top diagram) to a positive reference, which would allow a single op-amp to be used again, but that op-amp would need a negative supply to allow the output to go to zero.