There are some complexities here, and several possibilities.
First of all, it seems from the question that:
- There were not any "exigent circumstances" or any other special situation which would justify making a search without a warrant (there are several circumstances which can justify a warrantless search, but none are mentioned in the question).
- The police had no probable cause, indeed not even any reasonable suspicion. Thus the police had no valid reason even to request a warrant, and if they had asked for one, they should have been refused.
- No resident of the house consented to any search at any point.
- The police had no honest belief that they were acting lawfully. They knew, or any reasonable police officer should have known, that they were acting unlawfully.
Now, let us consider some of the possibilities left open by the question. For purposes of discussion, let us assume that the house was owned by Bob and Carol, and no one else lived in it. There are several possibilities.
Case One: The evidence appears to implicate Bob. Bob is charged, and Bob's lawyer Joan makes a timely motion to suppress the evidence. The judge should hold a suppression hearing, and under these conditions, should suppress the evidence. The trial will go forward without it, or be dismissed if there is not enough other evidence to proceed.
Case Two: Much like Case One, but another group of police officers had good reason to suspect Bob, and was already in the process of preparing a request for a warrant, supported by valid probable cause. Had the first group not searched the house unlawfully, the second group would have obtained a valid warrant and found the evidence under its authority. In this situation, known as inevitable discovery the evidence would be admitted, and the unlawful search will not matter.
Case Three: The evidence implicates Fred, not Bob or Carol. Fred did not live in the house, but had asked Carol to store some boxes for him. Carol did not know what was in them. Fred has no privacy rights to the house. Bob or Carol could have lawfully consented to a search, and Fred would have no grounds to object. Fred has no grounds to suppress the evidence, as Fred's rights were not violated, and Fred cannot assert Bob or Carol's rights. A trial of Fred would proceed as if the search had been lawful. Bob and Carol may have grounds for a Section 1983 lawsuit against the police for violation of their rights, but that will not help Fred.
Case Four: The evidence appears to implicate Bob. The police arrest Bob, and tell him that they have a case against him, and that if he does not confess, they will also arrest Carol as an accomplice. (They lie, but Bob believes them.) Bob pleads guilty. The unlawful search is never raised, and Bob is sentenced as if it had been lawful.
Case Five: The evidence appears to implicate Bob. Bob's lawyer Joan fails to request a suppression hearing, or to object at trial to the evidence from the unlawful search. Or more likely, instead of going to trial, Bob's lawyer arranges a plea bargain without raising the issue of the search. Bob is convicted as if the search had been lawful. Bob may have a valid appeal on the grounds of ineffective assistance of counsel, as Joan should have known better.
Case Six: The evidence appears to implicate Bob. But the police have other evidence as well. Bob's lawyer raises the issue of the unlawful search. However, the prosecutor convinces Bob's lawyer Joan that they can probably convict Bob even without the evidence from the search. Joan arranges a plea bargain, and Bob accepts it. Bob will be sentenced under the plea deal, and nothing will be done about the unlawful search, except that Bob may get a somewhat better deal because the authorities do not want it exposed in court.
Note that only in cases One and Five will a possibly guilty person possibly go free because of the unlawful search, and it is by no means certain even there.
It is also possible that a judge will wrongly admit the evidence in a Case One situation. This is likely to be corrected on appeal, with the unlawfulness as blatant as the question assumes. In a case where the unlawfulness is more marginal, this is less sure.