But your theory doesn't hold water.
Thom was a court bard. In the bardic tradition, a bard is an historian. Bards retain history through stories and songs. In RL, bards were travelling story tellers who maintained the history of the land through oral tradition. The fact that he was court bard to the Andoran court means he had to remember a lot of history. As for his knowledge of Fain, they both travelled widely and would have surely have encontered each other periodically.

If you read Towers of Midnight, you'll understand Thom better. I won't give any spoilers for those who haven't had the chance to read the book yet.

Being a darkfriend, and having a dislike for Aes Sedai is not the same thing. Thom's nephew was gentled by Red Ajah, and subsequently died. That is enough to cause a deep seated dislike for Tar Valon.
Think aboout it like this; Let's say you had a favorite Nephew, who decided to hang with a rough crowd. He's a good kid, doesn't get into trouble, just hangs out. One night, the cops decide to raid the hangout, where there are drugs. Your nephew just happens to be there. He's not selling, not running the crap, doesn't even touch a gun. When the cops burst in, some idiot starts shooting, and your nephew gets shot and killed.
As a result, you may develop a hatred for the police, even though they were doing their jobs keeping the streets safe. Your nephew was just in the wrong place, at the wrong time, with the wrong crowd. Your hatred for the police doesn't make you a criminal, it just means you hate the people who killed a member of your family.
Even with a deep seated hatred for police, you might eventually put the past aside, realizing that the cops weren't trying to kill your nephew. If some bonehead hadn't started shooting, he'd have been arrested, tried and possibly have been able to prove his innocense. The hatred in this case is misplaced, since the police were reacting to a shooter, and were defending themselves. Your nephew was caught in the crossfire, and a cop under fire isn't going to ask who has the guns, and if they're loaded.

Yah, I know, longwinded explanation. Thing is, Thom suffered a loss, and developed a dislike for Aes Sedai, especially the reds, who were the ones who killed the boy. And, as we have seen, the reds sometimes go to the far extreme. You never see Thom act disrespectful toward Aes Sedai, he's just wary of them, and treats most with respect.
If he was such a darkfriend, he would make sure he was attached to Rand, where his influence could be felt, not Mat.