OK, but if you start out an exercise by saying that base rod-height is irrelevant, then you are also implying that rover rod-height is irrelevant as well.
i.e. If you did a survey exercise with base and rover on two rods of unknown length, then the resulting elevations would be relative to each other, and not tied to a control-point; “floating” if you will.
BUT if you held those two rods side-by-side and saw that they were of equal length, then yes, you could tie the surveyed elevations to a control point.
(effectively the same as base-shift)
Take it one step further and even if those two rods of unknown length were not the same length, you could enter only the difference in their length as rover antenna-height and leave base antenna-height at zero, and get proper results.
At this point is is more about understanding and less about practicality. But I suppose if, during your travel on the way to a job, someone had relieved you of your poles/rods from the back of your truck; and then you managed to borrow two broomsticks that worked for poles, then you could still be confident about getting your elevations.
(and here is the cue for someone else to talk about plumbing a broomstick)