Do not connect Vdd and Vss with AD732x ADC?
The device will function but it will probably not function and meet all the spec's in the datasheet (noise, current, power and/or common mode range). The lifetime of the device may also be reduced or if there were a fault it could burn up. You can run a device in any configuration, but it most likely won't work as intended. If you ran the ADC through the same battery of tests (all the tests that they use to produce the graphs and the spec table), then you will most likely find that some of them are different.
It's not surprising that the AD7323 still functions, they have probably tied the digital VCC to the internal amp (or have a regulator) so if either the analog or digital power comes up first it doesn't cause problems for the circuitry (and AGND and DGND are probably tied if they were ohmed out with a meter, or with diodes, because it says that they can't be separated by more than 0.3V this usually indicates a diode turning on). Another thing is if you tried all selectable range settings, its likely that some of them will not function.
If you want, you could run the chip without connecting Vss and Vdd and even launch it in a product (I am not condoning this, I'm just saying that its a possibility), but if the chip fails or does not work as intended then the responsibility rests on the designer especially if they don't follow manufacture recommendations.