Hint: It is either NOT GOOD or insignificant.
If a job of significant size (> ½ mile) is designed in say ‘Utah South NAD83’, don’t do a site calibration (localization) using a Transverse Mercator base projection.
And don’t trust your data collector to ‘do the right thing’ without your intervention, many don’t. In fact, most do the wrong thing by default!
I have struggled to find a good example of why a localization needs to be based on the same projection as a larger project (say larger than 1 mile in any direction) is designed in. I think that reducing the example to a straight line between two points is the simplest method. [ What happens if you use the Wrong Base Projection … ]