Yes, but that hurts your argument rather than helping it. The drug dog does not, by itself have to clear the probable cause hurdle. Rather, the totality of the circumstances has to yield probable cause: https://en.wikipedia.org/wiki/Illinois_v._Gates.
So say the base rate for carrying drugs is 10% in the population. The police, based on their suspicions, pull over a population of people where 40% are carrying illegal drugs. Then, the drug dog comes in, and he's barely better than a coin flip--60% correct. Out of 100 people stopped, he'll correctly identify 24 of the 40 carrying drugs, and incorrectly flag 24 of the 60 not carrying drugs. But overall the process will be right 50% of the time, versus only a 10% probability if you stopped drivers at random. That's probable cause.
For example, let's say that the dog is not sufficient probable cause. Consider the cases:
1) drug dog indicates + suspect driving erratically
2) drug dog indicates + "I just have a feeling"
Am I correct that 1) might be PC but 2) could not be, no matter how accurate that officer turns out to be in practice?
(In case 2, the dog's finding more drugs than the base rate would not validate its accuracy, as the results are being pre-filtered to have a very different distribution.)
So rationally, the cop's "spidey sense" is indeed evidence. The question I posed to you (and whoever's reading) was whether it counts as legal evidence. And it's my understanding that, no matter how good your spidey sense is, it does not become PC in a legal sense until it is articulable. As Thomas Moore said in A Man for All Seasons:
"The world must construe according to its wits; this court, according to the law."
https://en.wikipedia.org/wiki/Receiver_operating_characteris...
There is some aggregate base rate, which is the percent of a random sample of motorists that are carrying drugs.
Then there is the rate of those who are actually carrying drugs within the a group that the police have pulled over, and suspect are carrying drugs, and have also presumably asserted their rights and refused a consensual search by the police and also do not have some other attribute (such as smell, items visible in plain view) that would provide probable cause.
You argue that "the base rate for drug possession in a car is almost certainly a tiny fraction of that" but in fact the base rate within this much narrower second group should be extremely high in comparison to the general population. And the problem is that searching that group, regardless of what you think of them, is illegal.
In order to make it legal you have to be able to show that you're going to do something specific that will provide probable cause.
Showing that the dog is anything short of a clearly reliable and accurate means of determining that a law is being violated means that the dog is not providing probable cause. A dog that alerts to drugs more 90% of the time when only 60% or so of the population in question has the drugs, has shown results that aren't sufficiently correlated to the data it is supposed to discern.
When that is true it is just a tool for violating laws that prohibit searches.