I think this is an ineffective defense, for the simple reason that there are probably some homes that aren't currently occupied by their owners but being searched anyway. Not being there, they obviously aren't giving consent.
Again, the more appropriate response is that this is a situation of hot pursuit, and it's a longstanding precedent that police may enter a home without a warrant during hot pursuit if they have reason to believe lives may be in danger. There's no constitutional violation, unless you want to quibble over the definition of "hot pursuit" -- but in this case, I think the definition would stand up.
Now, if the police were searching these houses, seizing evidence unrelated to the suspect being pursued, or making arrests based on that evidence, I would certainly mount strong objections to that. But as far as I know, there's no suggestion that that is happening. As long as they're entering houses specifically to find and arrest the armed and dangerous criminal they've been pursuing for the last several hours, I don't see a problem, and neither, I think, would the Supreme Court.