I am sure that in court the police would rely on the exigent circumstances exception to the 4th amendment.
Applies to hot pursuit only. Once they lost the suspect they have failed. They could set up roadblocks around the area and inspect cars for the suspect. There's no exigent circumstance that allows a sweep of multiple houses. There have been cases upheld where police "gut feel" justified searches of a specific house.
Not only does this violate the homeowners rights, but it is a great way to have evidence against the suspect thrown out by a court because it was gathered during an illegal sweep.