i'm sorry but no, thats utter crap, completely incorrect. What you say simply makes no sense, infact everything you've suggested in this thread makes no logical sense at all, based on the fact that if you were right, essentially police have every right to search any house they want at any time and they could simply say they were looking for someone they did have an arrest warrant out for. Seeing as thats not the case, and millions of people aren't complaining about that ridiculous abuse of power, it isn't happening.
Someone dropping drugs on the ground does not give anything even close to reasonable ground that there maybe other drugs on the premises, at all. If it did, why are drug cases so hard and take so long, why do they need to get multiple people leaving a house with drugs on them to make a case before they GET A SEARCH WARRANT to take down a drug house. By what you've said drugs cases would be easy, find one guy leaving a suspected house with drugs on him and you would have every right to bust right in, catch them with drugs on the premises and slam the jail door shut. Again, that simply does not happen, at all, which simply indicates they do not have the power you are saying they have.