Only if they were consistently accurate, past the point where random and/or informed guesses gave 'above average' results. Even then, amongst 'all the psychics' it's entirely possible that one person is guessing correctly by chance, because, given enough time and guessers, someone will. It's like flipping a coin, if enough people are doing it (say two million),
someone will get 20 heads in a row. Probably
If this a "wild talent" a la fort, then current statistical methods to determine if a non-random event was happening will not be sufficient. I suspect that changing the qualifying contributing factors will be necessary. An example of this would be an event of emotional importance to the seeker which has recently occurred.
As I recall, but can't remember the documentation, above average guesses have already been documented, in large numbers of trials. This was not in psychics dealing with a seeker, but in guessing cards or numbers. The anomalous results were slight but consistent; in other words, statistically significant. If one claims that, with additional trials, this significant result would disappear, this then drifts into the realm of nonfalsifiability. Poor science.
@Coal, I have had a few paranormal events happen to me, personally, with no other person acting as a psychic and relaying the information to me. The information was perceived by me directly in a flash or in a dream, and was not sought nor expected. The information was always about future events which were unimaginable, unexpected, and undesired. It was never wrong. I have had no false positives so far. Since I have told the universe who gave this to me to fuck off and stop it, the incidences have dropped to almost nothing. (Thank God. It is dreadful to see an imminent death and be able to do nothing to prevent it. Deaths by cancer and unusual accidents. It once saved my life, though, from an unexpected traffic accident.)
There is a certain Paul on the road to Damascus quality about the divide between people who have experienced this and people who have not.
I am a scientist and understand designing, qualifying, and evaluating evidence. So are you. The difference between us is that I have had anomalous experiences and you have not. I have had (more than) a single instance which rejects the null hypothesis. But I cannot prove it to you, and since I can't control when this happens, I cannot demonstrate this in controlled conditions. Perhaps others can - I hope so.
I think your premise is not robust because it does not take into account the constraints of the phenomena. You likely think my premise is not robust because I can't offer a way to force the phenomena into a shape which your view of science can examine.