voltage [or E for short
The KWH meter you are describing is used for 3 phase 4 wire systems [Wye systems, like 208Y/120, 480Y/277 and 600Y/347].
The total power is an Algebraic sum of all three readings under all conditions of load and power factor... the Wye system requires one wattmeter per phase - hence the 3 coils for a 4 wire system. Deltas and 3 wire Wyes can use a 2 coil type meter.
With all this said, I'll dive into your Q. [finally
If the phases were switched at the meter [for the non-external CT meters], this should not have any effect to the meter's accuracy or operation.
Same should be true for externally CT'ed meters.
I think the problem would be if the voltage taps were mix matched [A on B, etc.]. That would throw the meter out of whack, since the E is not referenced to the I correctly.
In my opinion, this would act like a really low power factor to the meter, plus the inaccuracies of true power measured would be either 2/3 too low or too high [depending on the mistaken connections].
Or it might just throw 180 degree pulsations straight into the rotating register, causing it to stall.
This is only my opinion for mistakenly connected voltage taps on external instrumented meters [meters run by external CTs]. Swapping the positions of the incoming feeders as they land in the lugs should have no effect to the meter [only to synchro'd induction motors!].
As far as I can remember, the 3 stator watthour meters function only as an Algebraic device under any and all loads and power factors, so if I am remebering correctly, they should not have any bearing to lead/lag frequencies of other phases [phase timing relationships].
I'll look through the trusty old EE handbooks to check up on this.
Someday I'll post some meter schematics!!! Anyone in the group an AutoCAD user???
More accurately, Any AutoCAD users that would like to take on some "pro bono" grunt work??? The grunt work would be schematic setups and edits for posting here in the forum.