Yes and no. There are a number of ways in which illegally obtained evidence, or FOTPT evidence can still be admitted. These are: attenuation, independent source

Yes and no. There are a number of ways in which illegally obtained evidence, or FOTPT evidence can still be admitted. These are: attenuation, independent source, inevitable discovery, and good faith. Roughly stated, attenuation is when something is too far down the line of causation, time, or there is a voluntary act of free will by the defendant to separate the illegality from the evidence, and the balance rests in favor of admission. Independent source is kind of like parallel construction: if the investigator also discovered the evidence in a legal way completely independent of the illegal search, the evidence will be admitted. Inevitable discovery extends this to evidence which, despite not being discovered legally, would have discovered the evidence regardless of the illegal search. Finally, the good faith exception will allow in evidence where law enforcement is relying in good faith on a warrant which is defective, or that they are proceeding legally pursuant to common law or statute. I've mostly summarized here the sides of the coin that will admit evidence poisoned by an unlawful search, but there are other doctrines that will tip it into the excluded category.