Can a differential ADC replace an instrumentation amplifier?
Think of it this way. The ADC is like a ruler, the instrumentation amplifier is like a magnifying glass. The amplifier takes a small signal and "magnifies" to a size that the ADC can easily "measure". 

Most ADCs like their inputs to sit around some voltage (the common mode voltage) so when you have a differential signal, one pin swings above the common mode voltage while the other swings below it. ADCs tend to have limited common mode ranges.

Instrumentation amplifiers are a special class of differential amplifier. They have very, very high input impedances (good for really weak signals). Instrumentation amplifiers are designed to amplify tiny differential signals which can have very large common mode voltages, something that is very hard with regular single ended amplifiers. The amp separates the part of the signal we want from the part we don't want and scales it to a range that the ADC can use.

E.g. Driving the sensor would yield a 5V common mode voltage. Your signal is differential so at full scale you'll see 4.990V on one pin and 5.010V at the other. this gives 20mV as 5.01 - 4.99 = 0.02 or 20mV.

Now, we want to convert that 20mV differential signal to single ended and scale that to 0-3.3V as that is the default input range of our ADC. That's where the instrumentation amp comes in, it will pick out the tiny 20mV signal and by setting it's gain to ~1600 that will let the ADC use it's full range i.e. the full 32k counts. As an added bonus, now that your signal is in the range of 0-3V or so, just about any micro can read it as just about all of them have internal ADCs anyway.