I'm wanting to do acquisitions of both parallel and perpendicular polarized FTIR samples to get the relative orientation of the amide with respect to the membrane.
I reflected a while on your question, therefore my answer is a bit late.
My general answer: please figure that out by experiment.
I think due to the fact that in general the linear polarization state at total reflection is changed you will get elliptical polarized light of unknown state after multiple total refections in your system. To my opinion a polarizer (analyzer) in front of the detector makes no sense here.
On the other hand at special cases such as parallel and perpendicular impingement of polarization onto your sample surface the polarization state will be conserved. Thus even after multiple total reflections linear polarized light will show up at the detector. Also here an analyzer should not be necessary.
But achieving perfect parallel and perpendicuclar polarization is not easy; you have to play around with angle of incomming linear polarization and have to check for the (linear) polarization state at the detector. For these experiments however it is necessary to have an analyzer placed there. When having 'zero' signal at the detector (at crossed polarizer configuration) you are sure to have linear polarized light.
I won't remove the analyzer yet; only turning the analyzer into parallel polarizer configuration and perform the experiments. Just by 90°rotation the polarizers you are able to do the complement experiment(s).