Can fully differential amplifiers with noise figures of up to 13dB be used to drive a high-speed 16-bit ADC without impacting performance?

Because of the lack of a common load resistance it is hard to use Noise Figure to compare an ADC with an amplifier. 

The other way to look at it is to use the input referred noise voltage of the ADC and compare it with the output noise of the amplifier (after the filter).  If the amplifier output noise is 30nV per root Hertz and there is 6dB of loss due to filter and termination then the amplifier noise voltage at the ADC input is about 15nV/ rt Hz.  If the ADC input voltage noise is over 30nH/ rt Hz the driving amplifier is not going to contribute significant noise.

This comparison only works with an anti alias filter.  Otherwise the amplifier noise will alias back and several Nyquist bands worth of noise will fold into the ADC signal.  If the amplifier has sufficient gain the anti alias filter won't impact the amplifier noise figure much. 

An ADC with 250MSPS clock and an SNR of 72dBFS has about 32nV/rt Hz of input noise.

To get voltage noise from SNR  use:  Vn = Vfs/(2*SQRT(2)) * 10^-(SNR/20)

Where Vfs = full scale input voltage and SNR is in dBFS.  To get the noise in volts per root hertz divide the noise by the square root of the Nyquist bandwidth. 

One thing to note is that the effective input noise of many high speed ADCs is dependent on the frequency of the sampled signal (and also clock speed).  It's important to compare the ADC performance at the deisred frequency.  Most amplifiers, on the other hand, have pretty flat noise over frequency as long as you are sufficiently over the 1/f corner.  The amplifier datasheet should give output voltage noise over frequency. 

When discussing Noise Figure it is necessary to specify the impedance.

I agree, but many people are familiar with 50 Ohm systems and don't necessarily consider exactly what happens to voltage for a given power level as the impedance changes. 

I've found it useful to make sure to keep the voltage levels in mind as the signal path approaches the ADC input.  For certain parameters, like full scale input, the voltage presented at the ADC is the only thing that matters.  For other parameters like SFDR, the impedance of the signal source at the ADC inputs is quite important.  I think that for noise the noise voltage at the ADC input terminals is more important than the noise power at the ADC input terminals, so for that particular metric the impedance is not very important.  That is why I like to use volts/ root hertz for noise at the ADC input instead of using noise figure.  I also think that aliasing is not captured in noise figure specs, so for making filter decisions the noise votlage/ root hertz is easier for me to use than noise figure. 

Does this make sense? 

Yes, Loren-- no argument about that. I just wanted to point out the necessity of specifying the impedance when duscussing noise figure. For example, a JFET op amp like an OPA827 may have a high noise figure in a 50 ohm system but if the impedance is raised to 100M, its noise figure becomes incredibly low.