Suppose I have a device with a number of ICs (microcontroller, logic gates, MEMs sensors, etc) which can operate from a supply voltage in the range of, say, 1.7V to 3.6V. Will the current draw be different if I power the devices at the low-end (1.7V) vs the high-end (3.6V) of the operating range? Does the answer vary depending on the specific IC or is there a general rule-of-thumb?
The datasheets I've looked at don't seem to go to this level of detail, and instead only specify current draw at a single supply voltage. I'm interested because my device is battery powered and I'm considering whether to run direct from the battery or to use a LDO regulator.