MAX2769 XTAL Reference Frequency
MAX2769 and MAX2769B can accommodate any reference frequency between 8 and 44 MHz. A PLL with 12 fractional bits, the sample rate and the IF bandpass filter are all configurable via SPI and you can realize a wide range of frequency plans. See datasheet.
16.368 MHz gives a very simple frequency plan, you can run the PLL in integer mode and sample at only 8MS/s, lowering computational load in the correlators.
Different frequency plans allow you to reduce beating from quantization noise, on the other hand they may introduce spurs in the IF from the fractional PLL. If you want to squeeze out the last decibel, I would try to avoid the prime factor 1023 in XTALS and go for a more elaborate setup.
Just to make sure I answer to your precise question: IF would be shifted by 96kHz, the complex bandpass would still let this pass. Taking the altered sample rate into consideration, the correlators would (for doppler 0Hz) see the phasor advance by 1.5338 rad per sample instead of by \$ \pi / 2 \$ per sample. This would be well outside the expected doppler range for ground based receivers and --- depending on software --- you would simply not acquire the signal ... although it is possible to receive it with software modifications.