I'd expect most half-heartedly comply. If told to go door to door, how many are going to have the stomach to search when the owner says "I have nothing"?
There will be some who enthusiastically bust folks, and some who look the other way. I'd think almost all would rather do real policing, though.
Police hear "I've got nothing," and "It wasn't me," and "That's not mine," all day, every day so it isn't likely to make a difference.