While you will get the full resolution between 0 and 1.1
True, it wasn't a good choice of words on my part. However, analogRead will not be able to discriminate values above AREF/1.1V (they will all read as 1023).
As long as your choice of AREF (e.g. Vcc) is tied to the voltage reference of your sensor, analogRead is fine, even if the reference itself is changing. So powering directly from a battery (bypassing the regulator) may not have ADC issues at all in the default configuration.
If your sensor on the other hand is ratiometric to some other independent reference, you will have problems unless your choice of AREF remains fixed or ideally use the very same reference (never above Vcc however) for its ADC conversions.
For someone powering his Arduno from a battery, it seems likely that attached sensors will be powered from the same source and typically these sensors will output a signal ratiometric to supply voltage. If this is the case, and using the 1.1V internal reference, analogRead levels will be influenced by a drop in battery voltage.