I would say your guess is correct; both gauges can be expected to have the same bias.
I seem to recall, vaguely, about having a pitot tube facing downstream to avoid the effect you are concerned about but that is probably gilding the lily.
What you can expect to find, I think with this experiment is that your pressure drop remains fairly linear with flow rate up to a certain point and then drops dramatically. The drop is when the flow is fast enough that turbulent flow not laminar flow occurs; although I think this is dependent on the pipe diameter and the viscosity so you may not see any change.
An open mind is a virtue...so long as all the common sense has not leaked out.