The inputs can come up with the power supplies of the ADC as long as they are maintained within the limits. The effect is to make sure that the ADC is powered up and running before the analog signals are applied to the inputs (ie power the ADC before powering the buffer or signal to drive it).
In general, designing your circuit to the abs max table is not a robust design. These limits are the intended limits to say that damage will not occur if you are within the limits; not the limits that is optimal to design to. General you want to use recommended limits (if available) or back-off the limits to give some margin of error for your design.
The inputs cannot violate the voltage spec, irrespective of the current. Operating/function is not guaranteed outside or as a result of transitions outside the abs max limits.