You do not specify fluid, one phase or two-phase, temperature, pressure, batch-pumping/varying flow or regular flow under constant parameters, and choke or measuring purpose of orifice plates.
Specific to your question I suspect the orifice plates are for measurement purposes (delta p over plates).
In any case I suspect under circumstances (if plates are too near each other) you could have more turbulence on both plates if excentric than if 'lined up' centric or excentric.
If this is the case you might have a tendency of varying and more unaccurate mesurement if measuring purpose, varying with the degree of turbulence. If choking perhaps (extra) varying degree of choking with flow or perhaps turbulence or cavitation problems and extra wear.
Certain is, however, that the flow picture/flowlines will vary with the distance (long distance less or no influence) and orientation of the orifice plates and flow.
To get a more accurate answer on influnce the only way is to test out 1:1 on actual site against a 'neutral' calibration. (If this is at all possible in practice???)