Hooray! Thanks for asking that! I do want to answer that very question .... you must have read my mind! Hooray!
The answer to all is YES! YES! YES! YES!
Let the Jury hear it all ... even "fruit of a poisoned tree" or whatever the legal term is for evidence acquired in an improper way. Let it be explained to them, that the evidence was so acquirred, that they the Jury has a duty to discount it.
Prosecute the cops, penalize the cops who so acquire evidence -- but don't hold back a thing from a Jury.
This is a radical idea, I know, in present time -- but I beleive it was the rule when a Jury was called out as the method of criminal trial in our Constitution.
It is crazy for a Jury to walk out a day after its cerdict and say "Gee if we had only known ..." what was obvious to everyone else, or even to a number of people if not everyone. Such filtering unavoidably creates a great distrust of the due process of the system. The Jury must seek to speak in accord with ALL the facts.