Measurement of HI with a metric steel tape - ? of Does it Matter?
use a laser meter
I'll only address the last question. No it doesn't matter. You would have to have much more education, knowledge, and/or training in order to collect data for something where 2mm of vertical would matter. In other words if you were doing something where 2mm mattered it would be very obvious to you that it did matter.
If 2mm mattered for your work you would not be using GPS or a total station. You would need an automatic/digital level.
As a test for those who think a systematic error in measure up of 2mm doesn't matter, add 2mm to your total station measure up height for a couple of traverse setups and see what happens to your backsights.