Power consumption in voltage detector
Supply current is given by datasheet:



If you use the open-drain output, you'll need to add the pullup resistor current (only when output is low). 

If you use the CMOS output, which is push-pull so it doesn't require a pullup, you'll need to add any current drawn by whatever circuit is connected to the output. If this is the input of a CMOS chip, check its datasheet for input leakage current. This will probably be so tiny it will be safe to neglect it. Now, if you want to light a LED with the output, that's different.