ADS1x15 ADCs in differential mode?

Could someone clarify for me - can I use differential mode to measure full range of unmodified CT output?
That is can I pass +-5V to A1 and A2?
DataSheet says inputs accept +- V for differential mode.
But in other places it warns not to put voltages outside [GND:VCC] range...

Just had a lesson learned on that very topic:

So while I got by with +/- 50 mV to answer your question, no. Since you mentioned a CT you can offset the CT output, I assume a sine wave and then pass it in, that is a popular method.