You may have a good point. If you have an impressed current system installed, you will deposit materials onto cathodic sites. The question remains: How significantly will your monitoring results be effected?
I do not understand the equipment arrangement. I do not know what is being cathodically protected (i.e., in proposed system). I am assuming that you have a metallic well casing (probably carbon steel) that is the primary material to be protected. If the outside of the casing is being protected, then an internal screen is not going to get much current and not cause a significant problem.
If the well casing is a well coated carbon steel (i.e., with a non-conductive coating like paint), then the amount of current required for protection of holidays is probably minor, perhaps 1~3% of total surface. This would result in minimal effect on the accuracy of your monitoring.
If the stainless steel screen were electrically insulated from the primary circuit being protected, then you would not deposit any metals electrochemically. A dielectric (i.e., electrically insulating material like micarta, rubber, etc) could be used.